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Background: Obese patients with depression face higher risks of adverse events. However, depression is often misdiagnosed and undertreated in this group. This study aimed to identify predictors of depression and create a nomogram and calculator to assess depression risk in obese Americans. Methods: This cross-sectional study included 2674 patients from the National Health and Nutrition Examination Survey database (NHANES). These participants were randomly classified into the training and validation groups in a 7:3 ratio. Predictors were selected by LASSO and multivariate logistic regression analysis to create the nomogram. C-statistics, calibration plots, and decision curve analysis (DCA) were used to test the nomogram's discriminative ability, calibration quality, and clinical value. Internal validation with bootstrap resampling and external validation with the validation group were also conducted. Results: The training and validation group consists of 1871 and 803 participants. Depression was presented in 11.4 % (203/2674) of these participants. Seven predictors were found, including gender, hypertension, weekday sleep duration, poverty to income ratio, history of seeing mental health doctor, diabetes, and feeling sleepy during the day. The nomogram showed good discrimination, with the area under the receiver operating characteristic curve (AUC) of 0.817 (95 % CI: 0.786–0.848) (0.806 through internal validation and 0.772 through external validation) and good calibration (P = 0.536). The DCA further confirmed the nomogram's clinical usefulness. Conclusion: The nomogram and calculator effectively predict depression risk in obese Americans and can be used as auxiliary tools for early screening in primary care.

In this paper, we consider the existence and multiplicity of normalized solutions to the following pseudo-relativistic Schrödinger equations $ \begin{equation*} \left\{ \begin{array}{lll} \sqrt{-\Delta+m^2}u +\lambda u = \vartheta |u|^{p-2}v +|u|^{2^\sharp-2}v, & x\in \mathbb{R}^N, \ u>0, \\ \ \int_{{\mathbb{R}^N}}|u|^2dx = a^2, \end{array} \right. \end{equation*} $ where $ N\geq2, $ $ a, \vartheta, m > 0, $ $ \lambda $ is a real Lagrange parameter, $ 2 < p < 2^\sharp = \frac{2N}{N-1} $ and $ 2^\sharp $ is the critical Sobolev exponent. The operator $ \sqrt{-\Delta+m^2} $ is the fractional relativistic Schrödinger operator. Under appropriate assumptions, with the aid of truncation technique, concentration-compactness principle and genus theory, we show the existence and the multiplicity of normalized solutions for the above problem.

In this paper, we study the existence of multiple normalized solutions for a Choquard equation involving fractional p-Laplacian in RN. With the help of variational methods, minimization techniques, and the Lusternik–Schnirelmann category, the existence of multiple normalized solutions is obtained for the above problem.

We prove the existence and multiplicity of solutions for a class of Choquard-Kirchhoff type equations with variable exponents and critical reaction. Because the appearance of the critical reaction, we deal with the lack of compactness by using the concentration-compactness principle. In particular, we discuss the main results in non-degenerate and degenerate cases. And we apply combination of Krasnoselskii genus and the Hardy-Littlewood-Sobolev inequality to get the results of existence and multiplicity.

In this paper, we deal with a class of Kirchhoff-type critical elliptic equations involving the [Formula: see text]-sub-Laplacians operators on the Heisenberg group of the form M(∥DHu∥pp + ∥u∥ p,Vp)[−Δ H,pu + V (ξ)|u|p−2u] = λf(ξ,u) + |u|p∗−2u,ξ ∈ ℍn,u ∈HWV1,p(ℍn), where [Formula: see text] is the [Formula: see text]-sub-Laplacian, [Formula: see text], [Formula: see text] is the horizontal Sobolev space on [Formula: see text]. And [Formula: see text] is the homogeneous dimension of [Formula: see text], [Formula: see text] is a real parameter, [Formula: see text] is the critical Sobolev exponent on the Heisenberg group. Under some proper assumptions on the Kirchhoff function [Formula: see text], the potential function [Formula: see text] and [Formula: see text], together with the mountain pass theorem and the concentration-compactness principles for classical Sobolev spaces on the Heisenberg group, we prove the existence and multiplicity of nontrivial solutions for the above problem in non-degenerate and degenerate cases on the Heisenberg group. The results of this paper extend or complete recent papers and are new in several directions for the non-degenerate and degenerate critical Kirchhoff equations involving the [Formula: see text]-Laplacian type operators on the Heisenberg group.

In this paper, we study the existence of ground state sign-changing solutions for the following fourth-order elliptic equations of Kirchhoff type with critical exponent. More precisely, we consider \begin{equation*} \begin{cases} \Delta^2u - \left(1 + b\int_{\Omega} |\nabla u|^2 dx\right)\Delta u = \lambda f(x,u) + |u|^{2^{\ast\ast}-2}u &\text{in } \Omega,\\ u = \Delta u = 0 & \mbox{on}\ \partial\Omega, \end{cases} \end{equation*} where $\Delta^2$ is the biharmonic operator, $N=\{5, 6, 7\}$, $2^{\ast\ast}=2N/(N-4)$ is the Sobolev critical exponent and $\Omega \subset \mathbb{R}^N$ is an open bounded domain with smooth boundary and $b, \lambda$ are some positive parameters. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains.

In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problem with critical variable exponent. By using constraint variational method and quantitative deformation lemma we show the existence of one least energy solution, which is strictly larger than twice of that of any ground state solution.

Abstract In the present article, by using the fixed point technique and the Arzelà–Ascoli theorem on cones, we wish to investigate the existence of solutions for a non-linear problems regular and singular fractional q-differential equation (cDqαf)(t)=w(t,f(t),f′(t),(cDqβf)(t)), $$ \bigl({}^{c}D_{q}^{\alpha }f\bigr) (t) = w \bigl(t, f(t), f'(t), \bigl({}^{c}D_{q}^{ \beta }f \bigr) (t) \bigr), $$ under the conditions f(0)=c1f(1) $f(0) = c_{1} f(1)$, f′(0)=c2(cDqβf)(1) $f'(0)= c_{2} ({}^{c}D_{q} ^{\beta } f) (1)$ and f″(0)=f‴(0)=⋯=f(n−1)(0)=0 $f''(0) = f'''(0) = \cdots =f^{(n-1)}(0) = 0$, where α∈(n−1,n) $\alpha \in (n-1, n)$ with n≥3 $n\geq 3$, β,q∈J=(0,1) $\beta , q \in J=(0,1)$, c1∈J $c_{1} \in J$, c2∈(0,Γq(2−β)) $c_{2} \in (0, \varGamma _{q} (2- \beta ))$, the function w is Lκ $L^{\kappa }$-Carathéodory, w(t,x1,x2,x3) $w(t, x_{1}, x_{2}, x_{3})$ and may be singular and Dqαc ${}^{c}D_{q}^{\alpha }$ the fractional Caputo type q-derivative. Of course, here we applied the definitions of the fractional q-derivative of Riemann–Liouville and Caputo type by presenting some examples with tables and algorithms; we will illustrate our results, too.

OBJECTIVES: The enhanced recovery after surgery (ERAS) protocol recommends prevention of intraoperative hypothermia. However, the beneficial effect of maintaining normothermia after radical cystectomy has not been evaluated. This study aimed to investigate the efficacy of fluid warming nursing in elderly patients undergoing Da Vinci robotic-assisted laparoscopic radical cystectomy. METHODS: A total of 108 patients with bladder cancer scheduled to undergo DaVinci robotic-assisted laparoscopic radical cystectomy were recruited and randomly divided into the control group (n=55), which received a warming blanket (43°C) during the intraoperative period and the warming group (n=53), in which all intraoperative fluids were administered via a fluid warmer (41°C). The surgical data, body temperature, coagulation function indexes, and postoperative complications were compared between the two groups. RESULTS: Compared to the control group, the warming group had significantly less intraoperative transfusion (p=0.028) and shorter hospitalization days (p

In this article we study a class of Kirchhoff-type Schrodinger-Choquard equations involving the fractional p-Laplacian. By means of Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero under a suitable value of $\lambda$. The main feature and difficulty of our equations arise in the fact that the Kirchhoff term M could vanish at zero, that is, the problem is degenerate. To our best knowledge, our result is new even in the framework of Schrodinger-Choquard problems.

In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions, which tend to zero for suitable positive parameters.

In this paper, we consider the existence and multiplicity of solutions for fractional Schrödinger equations with critical nonlinearity in RN. We use the fractional version of Lions' second concentration-compactness principle and concentration-compactness principle at infinity to prove that (PSc) condition holds locally. Under suitable assumptions, we prove that it has at least one solution and, for any m ∈ N, it has at least m pairs of solutions. Moreover, these solutions can converge to zero in some Sobolev space as ε → 0.

In this article, we study the fractional q-difference boundary-value problems with p-Laplacian operator $$displaylines{ D_{q}^{gamma}(phi_p(D_{q}^{alpha}u(t))) + f(t,u(t))=0, quad 0 < t < 1, ; 2 < alpha < 3,cr u(0) = (D_qu)(0) = 0, quad (D_qu)(1) = eta (D_qu)(eta), }$$ where $0 < gamma < 1$, $2 < alpha < 3$, $01. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions.

By using fixed-point theorem for operators on a cone, sufficient conditions for the existence of multiple positive solutions for a third-order boundary-value problem on the half-line are established. In the case of the p-Laplace operator our results for p>1 generalize previous known results. The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative u'.

In this paper, we study the existence of positive solutions for the nonlinear nth-order with m-point singular boundary-value problem. By using the fixed point index theory and a new fixed point theorem in cones, the existence of countably many positive solutions for a nonlinear singular boundary value problem are obtained.

In this paper, we deal with a class of Kirchhoff-type critical elliptic equations involving the p-sub-Laplacians operators on the Heisenberg group of the form ... where ... is the p-sub-Laplacian, 1 < p < Q, ... is the horizontal Sobolev space on .... And Q = 2n + 2 is the homogeneous dimension of ..., λ is a real parameter, p* = Qp/(Q - p) is the critical Sobolev exponent on the Heisenberg group. Under some proper assumptions on the Kirchhoff function M, the potential function V and f, together with the mountain pass theorem and the concentration-compactness principles for classical Sobolev spaces on the Heisenberg group, we prove the existence and multiplicity of nontrivial solutions for the above problem in non-degenerate and degenerate cases on the Heisenberg group. The results of this paper extend or complete recent papers and are new in several directions for the non-degenerate and degenerate critical Kirchhoff equations involving the p-Laplacian type operators on the Heisenberg group. [ABSTRACT FROM AUTHOR]