Constant-Sign Lp Solutions for a System of Integral Equations

We consider the following system of integral equations $$u_i(t)=\int^1_0g_i(t,s)f(s,u_1(s),u_2(s),\cdots,u_n(s))ds,\quad t\in \lbrack 0,1\rbrack,1\leq i\leq n.$$ Our aim is to establish criteria such that the above system has a constant-sign solution (u₁, u₂, …, u _n) ∈ (L^p[0, 1])ⁿ, where the integer 1 ≤ p < ∞ is fixed. We shall tackle the case when f is ‘nonnegative’ as well as the case when f is ‘semipositone’. The above problem is also extended to that on the half-line [0, ∞) $$u_i(t)=\int^1_0g_i(t,s)f(s,u_1(s),u_2(s),\cdots,u_n(s))ds,\quad t\in \lbrack 0,\infty ),1\leq i\leq n.$$      

Constant-Sign Solutions of a System of Fredholm Integral Equations

We consider the following system of Fredholm intergral equations u _i (t)=₀ ¹ g _i (t,s)f _i (s,u ₁(s),u ₂(s),...,u _n (s)) ds, t[0,1], 1in. Criteria are offered for the existence of single, double and multiple solutions of the system that are of constant signs. The generality of the results obtained is illustrated through applications to several well known boundary value problems. We also extend the above system of Fredholm intergral equations to that on the half-line [0,) u _i (t)=₀ g _i (t,s)f _i (s,u ₁(s),u ₂(s),...,u _n (s)) ds, t[0,), 1in and investigate the existence of constant-sign solutions.     

一类延迟积分方程的渐近概周期解

积分方程解的性态是积分理论中一个重要而又基本的问题.其中关于方程的周期解、概周期型解的存在性问题更是具有重要的理论意义和应用价值.已有文献中,有的延迟是常数,而有的延迟虽为函数,但对延迟做了是概周期函数的假设.本文在某些延迟积分方程的概周期解的存在性的基础上,并利用渐近概周期函数的定义和不动点理论,讨论了一类延迟是渐近概周期函数的积分方程的渐近概周期解的存在性.     

一类积分方程的向量值遥远概周期解

讨论了向量值遥远概周期函数空间上一类积分算子的不变性,并应用此结果对一类积分方程的向量值遥远概周期解的存在唯一性进行了研究,得到了其遥远概周期解存在唯一的一个充分性条件.     

一类非线性延迟积分方程正的概周期型解的存在性

本文利用不动点理论,给出了一类非线性延迟积分方程正的概周期型解的存 在性条件.     

The Existence of Positive Almost Periodic Type Solutions for Some Nonlinear Delay Integral Equations

This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators （Ma, Y.： On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41（2）, 211-220 （1999]]. Some known results are operators.     

Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case

We consider the system of Fredholm integral equations

Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces

In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain that if the forces are periodic (almost periodic) with small amplitude, then the solution of the coupled system is periodic (almost periodic).     

Almost Periodic Solutions of Nonautonomous Linear Difference Equations

Explicit almost periodic solutions are obtained for a class of almost periodic linear difference equations. The stability characteristics of the almost periodic solution are investigated. The results are applied to a nonautonomous hyperbolic difference equation modelling the dynamics of a single species population in temporally varying environments.     

一类中立型积分方程的正的概周期解

本文利用混合单调算子中的迭代技巧,研究了一类中立型积分方程正的概周期解的存在性,以前相关结果得以推广.     

抽象泛函微分方程的权伪概周期解

本文利用算子半群理论和Banach不动点定理研究了一类具非局部条件的抽象泛函微分方程权伪概周期解的存在唯一性,所得结论拓展了已有结果.     

一类一阶和二阶微分方程的渐近概周期解

对于一阶微分系统u′+F(u)=h(t),其中F为R~n上的严格单调算子,本文给出了其渐近概周期解存在和唯一的一个充分条件和一个必要条件.特别,对于一阶微分系统u′+▽Φ(u)=h(t),其中▽Φ代表R~N上凸函数Φ的梯度,讨论了其渐近概周期解存在和唯一的充分必要条件,并且把一些结果推广到了一类二阶方程.     

二阶时滞微分方程的概周期解

结合运用Liapunov泛函，讨论了一类二阶时滞方程的概周期解，所得结果具有实际意义。     

Bounded and Almost Periodic Solutions of Linear High-Order Hyperbolic Equations

The present paper is devoted to investigating high-order strictly hyperbolic operators with nearly constant coefficients. The invertibility of these operators in spaces of functions uniformly bounded or almost periodic in time is established, provided the symbol of the operator in question has no roots in an open strip containing the real line. Under the additional condition that the strip coincides with a half-plane, exponentially decaying solutions of the nonhomogeneous equation with right-hand side of exponential decay are constructed. In the case of equations with constant coefficients the necessity of the derived conditions is proved. The results of this paper were announced without proofs in [SV].     

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.     

一类非线性微分方程渐近概周期解的存在性

利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性．在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论．从而得到的结果在一定程度上推广和改进了相关结果．     

一类具有反射变元的泛函微分方程的有界解和概周期解

利用指数二分法及不动点定理,研究了一类具有反射变元的中立型泛函微分方程的有界解和概周期解的存在性.