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Abstract This paper studies some quasilinear elliptic nonlocal equations involving Orlicz–Sobolev spaces. On the one hand, a new sub-supersolution theorem is proved via the pseudomonotone operator theory; on the other hand, using the obtained theorem, we present an existence result on the positive solutions of a singular elliptic nonlocal equation. Our work improves the results of some previous researches.

This paper considers a singular Kirchhoff equation with convection and a parameter. By defining new sub-supersolutions, we prove a new sub-supersolution theorem. Combining method of sub-supersolution with the comparison principle, for Kirchhoff equation with convection, we get the conclusion about positive solutions when nonlinear term is singular and sign-changing.

This paper deals with a nonlinear nonlocal parabolic system with nonlinear heat-loss boundary conditions, which arise in the thermal explosion model. Firstly, we prove a comparison principle for some kinds of parabolic systems under nonlinear boundary conditions. Using this, we improve a new theorem of the sub-and-super solution. Secondly, based on the new sub-and-super solution theorem, the sufficient conditions that the solution exists and blows up uniformly in finite time are presented. Then, we generalize some of the lemmas related to uniform blow-up solutions, which are used to introduce the uniform blow-up profiles of solutions. Finally, we give several numerical simulations to illustrate the existence and uniform blow-up of solutions.

Abstract In this paper, using variational method, we study the existence of an infinite number of solutions (some are positive, some are negative, and others are sign-changing) for a non-homogeneous elliptic Kirchhoff equation with a nonlinear reaction term.

In this paper, we are concerned with the existence, uniqueness and long-time behavior of the solutions for a parabolic equation with nonlocal diffusion even if the reaction term is not Lipschitz-continuous at 0 and grows superlinearly or exponentially at +∞. First, we give a special sub-supersolution pair for some parabolic equations with nonlocal diffusion and establish the method of sub-supersolution. Second, using the sub-supersolution method, we prove the existence, uniqueness and long-time behavior of positive solutions. Finally, some one-dimensional numerical experiments are presented.

Abstract In this paper, we present a theorem for some impulsive boundary problems with derivative dependence by the upper and lower solutions method. Using the theorem obtained, we consider the existence of positive solutions of some class of singular impulsive boundary problems.

Focusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation ut=Δu+a∫Ωupdx,x,t∈QT,n·∇u+guu=0,x,t∈ST,ux,0=u0x,x∈Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a,p>0 is constant, QT=Ω×0,T, ST=∂Ω×0,T, and Ω is a bounded region in RN,N≥1 with a smooth boundary ∂Ω. First, we prove a comparison principle for some kinds of semilinear parabolic equations under nonlinear boundary conditions; using it, we show a new theorem of subsupersolutions. Secondly, based on the new method of subsupersolutions, the existence of global solutions and blow-up solutions is presented for different values of p. Finally, the blow-up rate for solutions is estimated also.

In this paper, we study the nonlocal equation ∫RN|u(x)|2dxγΔu=λu+μ|u|q−2u+|u|p−2u, xinRN having a prescribed mass ∫RN|u(x)|2dx=c2, where N≥3, μ, γ∈(0,+∞), q∈(2,2∗), c is a positive constant, p, q∈(2,2∗) with p≠q and 2∗=2NN−2. This research is meaningful from a physical point of view. Using variational methods, we present some results on the nonexistence and existence of solutions under different cases p and q which improve upon the previous ones via topological theory.

This article considers elliptic problems of Kirchhoff-type. We give some new definitions of lower and upper solutions for the problem and establish the method of lower and upper solutions when the upper and lower solutions are well ordered, i.e., the lower solution is less than the upper one, and we also consider the case when the upper and lower solutions have opposite ordering. In addition we use the relation between the topological degree and strict upper and lower solutions in both cases and using this we obtain multiplicity results for nonlinear Kirchhoff-type elliptic problems.

Abstract In this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω. $$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)+\mu h(x) \quad \mbox{in } \varOmega, \\ u>0 \quad \mbox{in } \varOmega, \\ u=0 \quad \mbox{on } \partial\varOmega. \end{cases} $$ By using the sub-supersolution method together with the comparison principle for elliptic equations, we obtain several existence and nonexistence theorems. Our works improve the results in the previous literature.

In this paper, a special class of boundary value problems, −▵u=λuq+ur,inΩ,u>0, inΩ,n·∇u+g(u)u=0,on∂Ω, where 00 is a parameter. The existence of the solution is verified via sub- and super-solutions method. In addition, the influences of parameters on the minimum solution are also discussed. The second positive solution is obtained by using the variational method.

Specialty fibers have introduced new levels of flexibility and variability in distributed fiber sensing applications. In particular, distributed acoustic sensing (DAS) systems utilized] the unique functions of specialty fibers to achieve performance enhancements in various distributed sensing applications. This paper provides an overview of recent preparations and developments of specialty-fiber-based DAS systems and their sensing applications. The specialty-fiber-based DAS systems are categorized and reviewed based on the differences in scattering enhancement and methods of preparation. The prospects of using specialty fibers for DAS systems are also discussed.

In this paper, we consider the existence of multiple solutions for second-order equation with Stieltjes integral boundary condition using the three-critical-point theorem and variational method. Firstly, a novel space is established and proved to be Hilbert one. Secondly, based on the above work, we obtain the existence of multiple solutions for our problem. Finally, in order to illustrate the effectiveness of our problem better, the example is listed.

This paper considers the output feedback stabilization for a cascaded-wave PDE-ODE system with velocity recirculation by boundary control. First, we choose a well-known exponentially stable system as its target system and find a backstepping transformation to design a state feedback controller for the original system. Second, we attempt to give an output feedback controller for the original system by introducing the observer. The resulting closed-loop system admits a unique solution which is proved to be exponentially stable. Finally, we give some numerical examples to prove the validity for the theoretical results.

Abstract In this paper, we consider the generalized logistic equation with nonlocal reaction term −Δu=u(λ+b∫Ωurdx−f(u))in Ω,u>0 in Ω,u=0 on ∂Ω. $$ -\Delta u=u \biggl(\lambda +b \int_{\Omega }u^{r}\,dx-f(u) \biggr)\quad \text{in } \Omega,\qquad u>0 \quad \text{ in } \Omega,\qquad u=0 \quad \text{ on } \partial \Omega. $$ Using the bifurcation and sub-supersolution method, we obtain the non-existence, existence, and uniqueness of positive solutions for different parameters on the nonlocal terms. Our works about the nonlocal elliptic problem improve the results in the previous literature.

Abstract In Raman distributed temperature system, the key factor for performance improvement is noise suppression, which seriously affects the sensing distance and temperature accuracy. Therefore, we propose and experimentally demonstrate dynamic noise difference algorithm and wavelet transform modulus maximum (WTMM) to de-noising Raman anti-Stokes signal. Experimental results show that the sensing distance can increase from 3 km to 11.5 km and the temperature accuracy increases to 1.58 °C at the sensing distance of 10.4 km.

In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case K(x)>0, as well as the monotonicity of the maximal solution on parameter λ. Thirdly, the uniqueness of the solution for K(x)<0 is proved, as well as the monotonicity of the solutions on parameter λ. Finally, we obtain some new results for the existence of solutions, and the dependence on the λ for the case K(x) is sign-changing.

In this article, using the sub-supersolution method and Rabinowitz-type global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.

In this article, we consider the singular elliptic boundary-value problem $$ -\Delta u+f(u)-u^{-\gamma} =\lambda u \text{ in } \Omega,\quad u>0\text{ in } \Omega,\quad u=0 \text{ on } \partial\Omega. $$ Using the upper-lower solution method, we show the existence and uniqueness of the solution. Also we study the boundary behavior and asymptotic behavior of the positive solutions.

In this article, we study the structure of global solutions to the boundary-value problem $$\displaylines{ -x''(t)+f(t,x)=\lambda ax(t),\quad t\in(0,1),\; t\neq\frac{1}{2},\cr \Delta x|_{t=1/2}=\beta_1 x(\frac{1}{2}),\quad \Delta x'|_{t=1/2}=-\beta_{2} x(\frac{1}{2}),\cr x(0)=x(1)=0, }$$ where $\lambda\neq0$, $\beta_1\geq\beta_{2}\geq0$, $\Delta x|_{t=1/2}=x(\frac{1}{2}+0)-x(\frac{1}{2})$, $\Delta x'|_{t=1/2}=x'(\frac{1}{2}+0)-x'(\frac{1}{2}-0)$, and $f:[0,1]\times\mathbb{R}\to\mathbb{R}$, $a:[0,1]\to(0,+\infty)$ are continuous. By a comparison principle and spectral properties of the corresponding linear equations, we prove the existence of solutions by using Rabinowitz-type global bifurcation theorems, and obtain results on the behavior of positive solutions for large $\lambda$ when $f(x)=x^{p+1}$.

The field of tunnel fire detection requires a Raman distributed temperature sensor (RDTS) with high-accuracy and visual localization. A novel temperature demodulation method to improve the temperature measurement accuracy of the RDTS systems is presented. This method is based on the optical dynamic difference compensation algorithm, which can eliminate the optical power fluctuation. In addition, the visual localization technology is presented by using the longitudinal lining model (LLM) of a three-dimensional (3D) temperature display, which enhances the engineering application of RDTS in tunnel fire detection. Experimental results indicate that the temperature measurement accuracy is optimized from 7.0 °C to 1.9 °C at the sensing distance of 18.27 km by using the presented method. We provide a solution for temperature field monitoring as well as fire visual localization of the tunnel through RDTS systems.

This article presents global properties and existence of multiple solutions for a class of boundary value problems of impulsive differential equations. We first show that the spectral properties of the linearization of these problems are similar to the well-know properties of the standard Sturm-Liouville problems. These spectral properties are then used to prove two Rabinowitz-type global bifurcation theorems. Finally, we use the global bifurcation theorems to obtain multiple solutions for the above problems having specified nodal properties.

In this article, we study the existence and uniqueness of the positive solution for a second-order singular three-point boundary-value problem with sign-changing nonlinearities. Our main tool is a fixed-point theorem.

Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular $m$-point boundary value problem $$ \left\{\begin{array}{ll} x''(t)+a(t)f(t,x(t),x'(t))=0,0

Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $m$-point boundary-value problem $$displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,quad 0

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: $$displaylines{ y''(t)+a(t)f(t,y(t),y'(t))=0,quad 0

Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem $$displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,quad 0

This paper considers the following boundary value problem: ((-u'(t))n)'=ntn-1f(u(t)), 01 is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.

In this paper, Krasnoselskii's theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.

Using a specially constructed cone and the fixed point index theory, this paper shows the existence of multiple positive solutions for a class of nonresonant singular boundary-value problem of second-order differential equations. The nonexistence of positive solution is also studied.

This paper considers the existence of positive solutions of the boundary value problems and , where and is a positive parameter. Using a time-map approach, we obtain the exact number of positive solutions in different cases.

Positive solutions to the singular initial-boundary value problems x′′=−f(t, xt), 0

Background: As common progenitor cells of osteoblasts and adipocytes, bone marrow mesenchymal (stromal) stem cells (BMSCs) play key roles in bone homeostasis, tissue regeneration, and global energy homeostasis; however, the intrinsic mechanism of BMSC differentiation is not well understood. Plasticity in energy metabolism allows BMSCs to match the divergent demands of osteo-adipogenic differentiation. Targeting BMSC metabolic pathways may provide a novel therapeutic perspective for BMSC differentiation unbalance related diseases. Scope of review: This review covers the recent studies of glucose, fatty acids, and amino acids metabolism fuel the BMSC differentiation. We also discuss recent findings about energy metabolism in BMSC differentiation. Major conclusions: Glucose, fatty acids, and amino acids metabolism provide energy to fuel BMSC differentiation. Moreover, some well-known regulators including environmental stress, hormone drugs, and biological and pathological factors may also influence BMSC differentiation by altering metabolism. This offers insight to the significance of metabolism on BMSC fate determination and provides the possibility of treating diseases related to BMSC differentiation, such as obesity and osteoporosis, from a metabolic perspective.

Osteoarthritis (OA) is a chronic joint disease characterized by the degeneration of articular cartilage and thickening and sclerosis of the subchondral bone. Mechanical factors play significant roles in the development and progression of OA, but it is still controversial whether exercise or rest is a more effective treatment for OA patients. In this study, we compared the effects of swimming and immobilization at different stages of OA in mice. Four weeks (the middle stage of OA) or eight weeks (the late stage of OA) after DMM (destabilization of the medial meniscus) surgery, the mice were subjected to four-week immobilization or swimming. Ink blot analysis and a beam walking test were performed to measure the gait and balance ability. Histological analysis was performed to determine the trabecular bone area, the thickness of subchondral bone, the thickness of the cartilage, the OARSI score, and the expression of MMP13 (matrix metalloproteinases) and IL-6 (interleukin). The results showed that at the middle stage of OA, both immobilization and swimming slowed down the progression of OA. Immobilization relieved OA to a certain extent by decreasing the production of regulatory factors to attenuate the degeneration of cartilage, which partly relieved the effects of DMM on gait, mainly in the hindlimb. Swimming mainly attenuated the thickening and rescued the area of subchondral bone.

Osteoporosis and sarcopenia (termed “Osteosarcopenia”), the twin-aging diseases, are major contributors to reduced bone mass and muscle weakness in the elderly population. Connexin 43 (Cx43) in osteocytes has been previously reported to play vital roles in bone homeostasis and muscle function in mature mice. The Cx43-formed gap junctions (GJs) and hemichannels (HCs) in osteocytes are important portals for the exchange of small molecules in cell-to-cell and cell-to-extracellular matrix, respectively. However, the roles of Cx43-based GJs and HCs in both bone and muscle aging are still unclear. Here, we used two transgenic mouse models with overexpression of the dominant negative Cx43 mutants primarily in osteocytes driven by the 10-kb Dmp1 promoter, R76W mice (inhibited gap junctions but enhanced hemichannels) and Δ130–136 mice (both gap junction and hemichannels are inhibited), to determine the actions of Cx43-based hemichannels (HCs) and gap junctions (GJs) in the regulation of bone and skeletal muscle from aged mice (18 months) as compared with those from adult mice (10 months). We demonstrated that enhancement of Cx43 HCs reduces bone mass due to increased osteoclast surfaces while the impairment of Cx43 HCs increases osteocyte apoptosis in aged mice caused by reduced PGE2 levels. Furthermore, altered mitochondrial homeostasis with reduced expression of Sirt-1, OPA-1, and Drp-1 resulted in excessive ROS level in muscle soleus (SL) of aged transgenic mice. In vitro, the impairment of Cx43 HCs in osteocytes from aged mice also promoted muscle collagen synthesis through activation of TGFβ/smad2/3 signaling because of reduced PGE2 levels in the PO CM. These findings indicate that the enhancement of Cx43 HCs while GJs are inhibited reduces bone mass, and the impairment of Cx43 HCs inhibits PGE2 level in osteocytes and this reduction promotes muscle collagen synthesis in skeletal muscle through activation of TGFβ/smad2/3 signaling, which together with increased ROS level contributes to reduced muscle force in aged mice.

Bone marrow mesenchymal stem cells (BMSCs) are multi-potent cell populations and are capable of maintaining bone and body homeostasis. The stemness and potential therapeutic effect of BMSCs have been explored extensively in recent years. However, diverse cell surface antigens and complex gene expression of BMSCs have indicated that BMSCs represent heterogeneous populations, and the natural characteristics of BMSCs make it difficult to identify the specific subpopulations in pathological processes which are often obscured by bulk analysis of the total BMSCs. Meanwhile, the therapeutic effect of total BMSCs is often less effective partly due to their heterogeneity. Therefore, understanding the functional heterogeneity of the BMSC subpopulations under different physiological and pathological conditions could have major ramifications for global health. Here, we summarize the recent progress of functional heterogeneity of BMSC subpopulations in physiology and pathology. Targeting tissue-resident single BMSC subpopulation offers a potentially innovative therapeutic strategy and improves BMSC effectiveness in clinical application.

Osteocytes could release some small molecules (≤ 1 kDa) through gap junctions and hemichannels to extracellular environment, such as prostaglandin E2 (PGE2), nitric oxide (NO) and adenosine triphosphate (ATP), which play key roles in transferring signals between bone cells and other tissue cells. Connexin (Cx) 43 is the most abundant connexin in osteocytes. To further discover molecules released by osteocytes through Cx43 channels and better understand the regulatory function of Cx43 channels in osteocytes, we performed non-targeted global metabolomics analysis using liquid chromatography-tandem mass spectrometry (LC-MS/MS) on conditioned medium collected from osteocytes isolated from two transgenic mouse models with Cx43 dominant negative mutants driven by a 10 kb-DMP1 promoter: R76W (gap junctions are blocked, whereas hemichannels are promoted) and Δ130-136 (both gap junctions and hemichannels are blocked). The results revealed that several new categories of molecules, such as “fatty acyls” and “carboxylic acids and derivatives”, could be released through osteocytic Cx43 channels. In addition, alteration of Cx43 channel function affected the release of metabolites related to inflammatory reaction and oxidative stress. Pathway analysis further showed that citric acid cycle was the most differential metabolic pathway regulated by Cx43 channels. In sum, these results isolated new potential metabolites released by osteocytes through Cx43 channels, and offered a novel perspective to understand the regulatory mechanisms of osteocytes on themselves and other cells as well.

Exposure to high altitude environment leads to skeletal muscle atrophy. As a hormone secreted by skeletal muscles after exercise, irisin contributes to promoting muscle regeneration and ameliorating skeletal muscle atrophy, but its role in hypoxia-induced skeletal muscle atrophy is still unclear. Our results showed that 4 w of hypoxia exposure significantly reduced body weight and gastrocnemius muscle mass of mice, as well as grip strength and the duration time of treadmill exercise. Hypoxic treatment increased HIF-1α expression and decreased both the circulation level of irisin and its precursor protein FNDC5 expression in skeletal muscle. In in vitro, CoCl2-induced chemical hypoxia and 1% O2 ambient hypoxia both reduced FNDC5, along with the increase in HIF-1α. Moreover, the decline in the area and diameter of myotubes caused by hypoxia were rescued by inhibiting HIF-1α via YC-1. Collectively, our research indicated that FNDC5/irisin was negatively regulated by HIF-1α and could participate in the regulation of muscle atrophy caused by hypoxia.

Bone–muscle crosstalk plays an important role in skeletal biomechanical function, the progression of numerous pathological conditions, and the modulation of local and distant cellular environments. Previous work has revealed that the deletion of connexin (Cx) 43 in osteoblasts, and consequently, osteocytes, indirectly compromises skeletal muscle formation and function. However, the respective roles of Cx43-formed gap junction channels (GJs) and hemichannels (HCs) in the bone–muscle crosstalk are poorly understood. To this end, we used two Cx43 osteocyte-specific transgenic mouse models expressing dominant negative mutants, Δ130–136 (GJs and HCs functions are inhibited), and R76W (only GJs function is blocked), to determine the effect of these two types of Cx43 channels on neighboring skeletal muscle. Blockage of osteocyte Cx43 GJs and HCs in Δ130–136 mice decreased fast-twitch muscle mass with reduced muscle protein synthesis and increased muscle protein degradation. Both R76W and Δ130–136 mice exhibited decreased muscle contractile force accompanied by a fast-to-slow fiber transition in typically fast-twitch muscles. In vitro results further showed that myotube formation of C2C12 myoblasts was inhibited after treatment with the primary osteocyte conditioned media (PO CM) from R76W and Δ130–136 mice. Additionally, prostaglandin E2 (PGE2) level was significantly reduced in both the circulation and PO CM of the transgenic mice. Interestingly, the injection of PGE2 to the transgenic mice rescued fast-twitch muscle mass and function; however, this had little effect on protein synthesis and degradation. These findings indicate a channel-specific response: inhibition of osteocytic Cx43 HCs decreases fast-twitch skeletal muscle mass alongside reduced protein synthesis and increased protein degradation. In contrast, blockage of Cx43 GJs results in decreased fast-twitch skeletal muscle contractile force and myogenesis, with PGE2 partially accounting for the measured differences.