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We prove the asymptotic properties of the solutions to the 3D Navier-Stokes system with singular external force, by making use of Fourier localization method, the Littlewood-Paley theory and some subtle estimates in Fourier-Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339 (2022)]. We deal either with the non-stationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier-Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339 (2022)] [ABSTRACT FROM AUTHOR]

In this paper, we consider an abstract third-order differential equation and deduce some results on the maximal regularity of its strict solution. We assume that the inhomogeneity appearing in the right-hand term of this equation belongs to some anistropic Hölder spaces. We illustrate our results by a BVP involving a 3D Laplacian posed in a cusp domain of ℝ4. [ABSTRACT FROM AUTHOR]

In this paper, we will extend the strict stability to impulsive differential equations. By using Lyapunov functions, we will get some criteria for the strict stability of impulsive differential equations, and we can see that impulses do contribute to the system's strict stability behavior. An example is also given in this paper to illustrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the set-contraction theory. [ABSTRACT FROM AUTHOR]

This paper proves that, under the hypothesisg(t, 0, 0)=0 and some natural assumptions, the generatorgof a backward stochastic differential equation can be uniquely determined by the correspondingg-expectations with all terminal conditions. The main result of this paper also confirms and extends Peng Shige’s conjecture. [ABSTRACT FROM AUTHOR]

In this paper, we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems X corresponding to the parameters ( Y, β, ψ), where Y is a Hunt process and ψ is the generating function for the offspring. The main tool of this paper is the spine decomposition and we only need an Llog L condition. [ABSTRACT FROM AUTHOR]

In this paper, we classify the set of Lorentzian metrics on T, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations. [ABSTRACT FROM AUTHOR]

Stochastic differential equations with the time average have received increasing attentions in recent years since they can offer better explanations for some financial models. Since the time average is involved in this class of stochastic differential equations, in this paper, the linear growth condition and the Lipschitz condition are different from the classical conditions. Under the special linear growth condition and the special Lipschitz condition, this paper establishes the existence and uniqueness of the solution. By using the Lyapunov function, this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate. Finally, a scalar example is given to illustrate the applications of our results. [ABSTRACT FROM AUTHOR]

Extending normal gamma and normal inverse Gaussian models, multivariate normal stable Tweedie (NST) models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of multivariate exponential families, the NST models are recently classified by their covariance matrices V(m) depending on the mean vector m. In this paper, we prove the characterization of all the NST models through their determinants of V(m), also called generalized variance functions, which are power of only one component of m. This result is established under the NST assumptions of Monge-Ampère property and steepness. It completes the two special cases of NST, namely normal Poisson and normal gamma models. As a matter of fact, it provides explicit solutions of particular Monge-Ampère equations in differential geometry. [ABSTRACT FROM AUTHOR]

In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T > 0; moreover, such a solution has T as its minimal period. [ABSTRACT FROM AUTHOR]

Let x: M n → R n+1 be an n(≥ 2)-dimensional hypersurface immersed in Euclidean space R n+1. Let σ i (0 ≤ i ≤ n) be the ith mean curvature and Q n = Σ(−1) i+1() σ σ i . Recently, the author showed that W n ( x) = ∫ M Q n dM is a conformal invariant under conformal group of R n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional W n is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in R 4 which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. [ABSTRACT FROM AUTHOR]

In this paper, under the most elementary conditions on a backward stochastic differential equation (BSDE for short) introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of "process", based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved. [ABSTRACT FROM AUTHOR]

In this paper, we first define a kind of pseudo-distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel-Carathéodory Theorem on any Riemann surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we first generalize Gerstewitz's functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904-937 (2014)]. By using the generalized Gerstewitz's functions and the partial order principle, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results. [ABSTRACT FROM AUTHOR]

In this paper, we study the well-posedness of the third-order differential equation with finite delay (P3): αu‴ (t) + u″(t) = Au(t) + Bu′ (t) + Fut + f(t)(t ∈ T:= [0, 2π]) with periodic boundary conditions u(0) = u(2π), u′(0) = u′(2π), u″ (0) = u″(2π), in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces Bp,qs(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠{0}, α ≠ 0 is a fixed constant and F is a bounded linear operator from Lp([−2π, 0];X) (resp. Bp,qs([−2π, 0];X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [−2π, 0]. Necessary and sufficient conditions for the Lp-well-posedness (resp. Lp-well-posedness) of (P3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Brownian motion risk model with interest. The Laplace transform of the first exit time from the upper barrier before hitting the lower barrier is obtained. Using the obtained result and exploiting the limitation idea, we derive the Laplace transform of total duration of negative surplus. [ABSTRACT FROM AUTHOR]

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n by employing the Li’s method of energy function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of g-variance and study some properties of this operator. We find the nonlinear variance operator, g-variance, does not preserve some basic properties of traditional mathematic variance. We also consider the relationship [Figure not available: see fulltext.] and [Figure not available: see fulltext.] Var Q[ ξ] ([Figure not available: see fulltext.] and [Figure not available: see fulltext.] Var Q[ ξ]). The result shows that the maximum (minimum) variance is not always equal to [Figure not available: see fulltext.]). If g satisfies some restrictive conditions, we get the uniqueness theorem and the comparison theorem via g-variance. [ABSTRACT FROM AUTHOR]

The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unlike the leading work of Black, certain trading rules are considered so as to be more fit for practical futures markets. The paper prices futures options with initial margin requirements and daily price limit by duplicating them with the help of the theory of backward stochastic differential equations (BSDEs, for short). Furthermore, an explicit expression of the price of the call (or the put) futures option is given and also is shown to be the unique solution of the associated nonlinear partial differential equation. [ABSTRACT FROM AUTHOR]

In this paper, Brin-Katok local entropy formula and Katok’s definition of the measure-theoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in H k (Ω, R 2) for any k ≥ 1, which attracts any bounded set of H k (Ω, R 2) in the H k -norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong’s conclusion. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation. [ABSTRACT FROM AUTHOR]

By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system where P( t), R( t), Q( t) are n × n real continuous matrix functions, P( t) and R( t) are commutative. The results improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper. [ABSTRACT FROM AUTHOR]

In this paper we give the existence of mild solutions for semilinear Cauchy problems u'( t) = Au( t) + f( t, u( t)), t ∈¸ I, a.e. with nonlocal initial condition u(0) = g( u) + u 0 when the map g loses compactness in Banach spaces. [ABSTRACT FROM AUTHOR]

Let Ω be a bounded or unbounded domain in R n . The initial–boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains. [ABSTRACT FROM AUTHOR]

In this paper, we first consider the least-squares solution of the matrix inverse problem as follows: Find a hermitian anti–reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X,B we have min A ‖ AX − B‖. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by S E . Then the matrix nearness problem for the matrix inverse problem is discussed. That is: Given an arbitrary A*, find a matrix  ∈ S E which is nearest to A* in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix. [ABSTRACT FROM AUTHOR]

We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [ABSTRACT FROM AUTHOR]

The existence, multiplicity and infinite solvability of positive solutions are established for some two–point boundary value problems of one–dimensional p–Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number. [ABSTRACT FROM AUTHOR]

In this paper, we develop the local linking theorem given by Li and Willem by replacing the Palais–Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems ℋ ü + A( t) u + ∇ V ( t, u) = 0, u ∈ ℝ N, t ∈ ℝ. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem. [ABSTRACT FROM AUTHOR]

In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation −u”(t) = f(t, u(t)), where f : R 2 → R is a continuous odd function and is 2π–periodic in t. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general ( α, β)-metrics, which are defined by a Riemannian metric $$\alpha = \sqrt {{a_{ij}}\left( x \right){y^i}{y^j}} $$ and a 1-form β = b ( x) y . We obtain the differential equations that characterizes these metrics with vanishing Douglas curvature. By solving the equivalent PDEs, the metrics in this class are totally determined. Then many new Douglas metrics are constructed. [ABSTRACT FROM AUTHOR]

This paper is divided in two parts: in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space ( V, ω). Successively, in Section 3, we apply our construction in the setting of Heisenberg groups ℍ, n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin's complex of differential forms in ℍ. [ABSTRACT FROM AUTHOR]

Let { X, X; n ≥ 0} be a sequence of independent and identically distributed random variables with E X = 0, and assume that E X I(| X| ≤ x) is slowly varying as x→∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series $$\sum\nolimits_{n = 0}^\infty {{\beta ^n}{X_n}\left( {0 < \beta < 1} \right)} $$ is obtained, under some minimal conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of functions called weighted pseudo S-asymptotically periodic function in the Stepanov sense and explore its properties in Banach space including composition theorems. Furthermore, the existence, uniqueness of the weighted pseudo S-asymptotically periodic mild solutions to partial evolution equations and nonautonomous semilinear evolution equations are investigated. Some interesting examples are presented to illustrate the main findings. [ABSTRACT FROM AUTHOR]

The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincaré returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the period-doubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2-homoclinic orbits. [ABSTRACT FROM AUTHOR]

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain. [ABSTRACT FROM AUTHOR]

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations. [ABSTRACT FROM AUTHOR]

In this paper, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous (left or right continuous) generator. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs. [ABSTRACT FROM AUTHOR]

In this paper, we study the solutions for Toda system on Riemann surface with boundary. We prove a sufficient condition for the existence of solution of Toda system in the critical case. [ABSTRACT FROM AUTHOR]

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed in little Hölder spaces. Next we investigate asymptotic behavior of the solution. By computing the spectrum of the linearized problem and using the linearized stability theorem, we give the rigorous analysis of stability and instability of all stationary flat solutions under the non-flat perturbations. The method used in proving these results is first to reduce the free boundary problem to a differential equation in a Banach space, and next use the abstract well-posedness and geometric theory for parabolic differential equations in Banach spaces to make the analysis. [ABSTRACT FROM AUTHOR]

In this paper, under the frame of Fu $$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{c} $$ik spectrum, we study the existence of periodic solutions for p-Laplacian equation by asymptotic behaviors of potential function, improve some results to some extent. [ABSTRACT FROM AUTHOR]

In this paper we consider the large time behavior of solutions to an n-dimensional transmission problem for two Kirchhoff type viscoelastic wave equations, that is, the wave propagation over bodies consisting of two physically different types of materials. One component is a simple elastic part while the other is a viscoelastic component endowed with a long range memory. We show that the dissipation produced by the viscoelastic part is strong enough to produce exponential or polynomial decay of the solution [ABSTRACT FROM AUTHOR]

In this paper, the differential equation involving iterates of the unknown function, with a complex parameter a, is investigated in the complex field ℂ for the existence of analytic solutions. First of all, we discuss the existence and the continuous dependence on the parameter a of analytic solution for the above equation, by making use of Banach fixed point theorem. Then, as well as in many previous works, we reduce the equation with the Schröder transformation x( z) = y( αy−1( z)) to the following another functional differential equation without iteration of the unknown function which is called an auxiliary equation. By constructing local invertible analytic solutions of the auxiliary equation, analytic solutions of the form y( αy−1( z)) for the original iterative differential equation are obtained. We discuss not only these α given in Schröder transformation in the hyperbolic case 0 < | α| < 1 and resonance, i.e., at a root of the unity, but also those α near resonance (i.e., near a root of the unity) under Brjuno condition. Finally, we introduce explicit analytic solutions for the original iterative differential equation by means of a recurrent formula, and give some particular solutions in the form of power functions when a = 0. [ABSTRACT FROM AUTHOR]

In this paper we construct Almansi decompositions for powers of the ultrahyperbolic operator. The construction will be done in a constructive way. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces. [ABSTRACT FROM AUTHOR]

This paper discusses nonlinear Schrödinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions. [ABSTRACT FROM AUTHOR]

This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval. The least words of given lengths, the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established. [ABSTRACT FROM AUTHOR]

In this paper, we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Rüssmann’s non-degeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth, with the same Gevrey index as the Hamiltonian. [ABSTRACT FROM AUTHOR]

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″+ e − z f′+ Q( z) f = F( z), where Q( z) ≡ h( z) e cz and c ∊ ℝ. [ABSTRACT FROM AUTHOR]