Almost Periodic Solutions of Nonlinear Second Order Differential Equations

We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions.     

Positive solutions of boundary-value problems for disfocal ordinary differential equations

We study the existence of positive solutions of a nonlinear eigenvalue problem for a two-point boundary-value problem for a family of second-order disfocal ordinary differential equations. We apply a cone-theoretic fixed-point theorem and obtain both sufficient conditions for the existence of positive solutions and sufficient conditions for the existence of multiple positive solutions.     

Periodic solutions of abstract functional differential equations with state‐dependent delay

In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and regularity of solutions for neutral partial functional integrodifferential equations with infinite delay

This paper is concerned with the existence and regularity of solutions for a class of neutral partial functional integrodifferential equations with infinite delay in Banach spaces. We use the theory of resolvent operator developed in R. Grimmer (1982) [29] to show the existence of mild solutions. We give sufficient conditions ensuring the existence of strict solutions. The phase space is axiomatically defined. Our results are applied to prove the existence and regularity of solutions to a Lotka–Volterra model with diffusion.     

Strong solutions of periodic parabolic problems with discontinuous nonlinearities

We study the problem of finding time-periodic solutions of a parabolic equation with the homogeneous Dirichlet boundary condition and with a discontinuous nonlinearity. We assume that the nonlinearity is equal to the difference of two superpositionally measurable functions nondecreasing with respect to the state variable. For such a problem, we prove the principle of lower and upper solutions for the existence of strong solutions without additional constraints on the “jumping-up” discontinuities in the nonlinearity. We obtain existence theorems for strong solutions of this class of problems, including theorems on the existence of two nontrivial solutions.     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

Existence of extremal solutions by approximation to a first-order initial dynamic equation with Carathéodory's conditions and discontinuous non-linearities*

This paper is devoted to the study of the existence of extremal solutions to a first-order initial value problem on an interval of an arbitrary time scale. We prove the existence of extremal solutions for problems satisfying Carathéodory's conditions. Moreover, they are approximated uniformly by a sequence of lower and upper solutions to this problem, respectively.

We also can warrant the existence and approximation of extremal solutions for the problem by relaxing their continuity properties.     

Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.     

Existence of solutions for discrete p-Laplacian with potential boundary conditions

We are concerned with the existence of solutions for some discrete p-Laplacian equations subjected to a potential type boundary condition. Our approach is a variational one and relies on Szulkin's critical point theory. We obtain the existence of solutions in a coercive case as well as the existence of non-trivial solutions when the corresponding energy functional has a ‘mountain pass’ geometry.     

抽象空间中无穷时滞微分方程概自守解的存在性

研究抽象空间中无穷时滞微分方程概自守解的存在性,证明了在正实轴上存在有界解蕴含存在概自守解,并给出了结论在L otka-V o lterra型方程中的应用.我们的结果推广了经典的关于非齐次线性概周期微分方程概周期解存在性的结论.     

Mathematics

We prove the existence of sign changing solutions of a semilinear elliptic eigenvalue problem with constraint by using variational methods. Among those three solutions we obtained, one is positive, one negative and one sign changing. We also prove the existence of multiple sign changing solutions under some additional condition.     

Multiple and sign changing solutions of an elliptic eigenvalue problem with constraint

We prove the existence of sign changing solutions of a semilinear elliptic eigenvalue problem with constraint by using variational methods. Among those three solutions we obtained, one is positive, one negative and one sign changing. We also prove the existence of multiple sign changing solutions under some additional condition.     

Cerami条件下脉冲边值问题古典解的存在性

在非线性项不满足Ambrosetti-Rabinowitz条件时研究脉冲微分方程边值问题,在原来的变分结构下,利用Cerami条件下成立的临界点理论来研究脉冲微分方程边值问题古典解的存在性和多重性.     

On conformally invariant equation( - \Delta )^p u - K(x)u^{\tfrac{{N + 2p}}{{N - 2p}}} = 0 and its generalizationsand its generalizations

We consider the question of existence and non-existence of positive entire solutions for conformally invariant equations involving polyharmonic operator. We obtain existence of infinitely many positive solutions if the potential decays sufficiently fast at infinity and the nonexistence of positive solutions if the potential grows too fast at infinity. We also establish a Kazdan-Warner type condition for non-existence of solutions decaying at infinity. Entrata in Redazione l'11 novembre 1998. Ricevuta nuova versione l'1 novembre 1999.     

Solvability of systems of volterra integral equations of the first kind with piecewise continuous kernels

We construct an asymptotic approximation for solutions of systems of Volterra integral equations of the first kind with piecewise continuous kernels. We use the asymptotics as an initial approximation in the proposed method of successive approximations to the desired solutions. We prove the existence of a continuous solution depending on free parameters and establish sufficient conditions for the existence of a unique continuous solution. We illustrate the proved existence theorems with examples.     

Traveling wave solutions in a delayed lattice competition-cooperation system

In this paper, we first reduce the existence of traveling wave solutions in a delayed lattice competition-cooperation system to the existence of a pair of upper and lower solutions by means of Schauder’s fixed point theorem and the cross iteration scheme, and then we construct a pair of upper and lower solutions to obtain the existence and nonexistence of traveling wave solutions. We also consider the asymptotic behaviour of any nonnegative traveling wave solutions at negative infinity.     

具非自治微小扰动的脉冲方程三个古典解的存在性

在半直线无穷区间上,我们研究具有微小非自治扰动项的脉冲方程边值问题的古典解,应用变分方法和相应的临界点理论得到了三个古典解的存在性.     

Affine-periodic solutions for discrete dynamical systems

The paper concerns the existence of affine-periodic solutions for discrete dynamicalsystems. This kind of solutions might be periodic, harmonic, quasi-periodic, even non-periodic.We prove the existence of affine-periodic solutions for discrete dynamical systems by using thetheory of Brouwer degree. As applications, another existence theorem is given via Lyapnovfunction.     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

Asymptotics and existence of bounded solutions of a nonlinear Schrödinger equation on the half-line

We study the asymptotics and existence of nonzero bounded solutions of the Schrödinger equation on the half-line with potential that implicitly depends on the wave function via a nonlinear second-order ordinary differential equation. We prove the existence of countably many nonzero bounded solutions on the half-line and derive asymptotic formulas at infinity for these solutions.