Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions.     

Large solutions of mixed sublinear/superlinear elliptic equations

We consider the equation Δu=p(x)uα+q(x)uβ on RN (N?3) where p, q are nonnegative continuous functions and 0<α?β. We establish conditions sufficient to ensure the existence and nonexistence of nonnegative entire large solutions of the equation.     

MULTIPLE POSITIVE SOLUTIONS TO BVPS FOR HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACES

1. IntroductionIn [1], F.H. Wong proved the ekistence of a nonnegative solution to a higher order scalarboUndary value problem (for short, BVP) by means of Schauder's fixed point theorem. Inthis article, we shajl investigate the ekistence of multiple positive solutions of such higherorder BVP in Banach space E by utilizing the conical expansion and compression foredpoied principle and the thed poied index theory, both completely dtherellt from that in [1].Consider the following higher ord…     

Multiple positive solutions for resonant difference equations

In this paper, we study the existence of multiple positive solutions for a class of resonant difference equations by using critical point theory.     

非齐次线性差分方程的Cm解[英文]

设c0,c1,…,cn均为实的常数，F（x)是个从R到R的C^m映射。本文讨论了非齐次线性差分方程∑i=1ncif(x i)=F(x)的C^m(m≥0）的存在性和唯一性。     

Multiple solutions for boundary value problems of second-order difference equations with resonance

In this paper, we study the existence of multiple solutions for boundary value problems of second-order difference equations with resonance at both infinity and zero by using Morse theory, critical point theory, minimax methods and bifurcation theory.     

Necessary and sufficient conditions for oscillation of first order nonlinear neutral differential equations

In this paper, we prove that every solution of the first order nonlinear neutral differential equation

     

On the solutions of a class of difference equations

In this note we investigate the solutions of a class of difference equations and prove that Conjectures 4.8.2, 4.8.3, 5.4.6 and 6.10.3 proposed by M. Kulenovic and G. Ladas in [M. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, Chapman & Hall/CRC Press, 2002] are true.     

Perturbations for linear difference equations

In this paper we study boundary value problems for perturbed second-order linear difference equations with a small parameter. The reduced problem obtained when the parameter is equal to zero is a first-order linear difference equation. The solution is represented as a convergent series in the small parameter, whose coefficients are given by means of solutions of the reduced problem.     

Multiplicity of positive periodic solutions to superlinear repulsive singular equations

In this paper, we study positive periodic solutions to the repulsive singular perturbations of the Hill equations. It is proved that such a perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.     

Asymptotic behavior of solutions of difference equations in Banach spaces

In this paper we consider the first order difference equation

and give necessary and sufficient conditions so that there exist solutions which are asymptotically constant. These results generalize those given earlier by Popenda and Schmeidel. As an application we give necessary and sufficient conditions for the second order difference equation

to have asymptotically constant solutions.

     

Two positive solutions of a boundary value problem for difference equations

We consider a second order vector boundary value problem for difference equations and establish criteria for the existence of at least two positive solutions by an application of a fixed point theorem in cones.     

Growth of meromorphic solutions of linear difference equations

In this paper, the authors continue to study the growth of meromorphic solutions of homogeneous or non-homogeneous linear difference equations with entire coefficients, and obtain some results which are improvement and extension of previous results in Chiang and Feng (2008) [7] and Laine and Yang (2007) [19]. Examples are also given to illustrate the sharpness of our results.     

Multiple positive solutions of boundary value problems for systems of nonlinear second-order differential equations

This paper is concerned with boundary value problems for systems of nonlinear second-order differential equations. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.     

Existence of positive solutions for nth-order periodic difference equations

This paper is devoted to the study of difference equations coupled with periodic boundary value conditions. We deduce the existence of at least one positive solution provided that the nonlinear part of the equation satisfies some monotonicity assumptions and the existence of a positive upper solution. The result is obtained from a new fixed point theorem based on the classical Krasnoselskii's cone expansion/contraction theorem and the constant sign properties of the related Green's function.     

Oscillation of second-order nonlinear neutral differential equations

In this paper, some sufficient conditions for oscillation and nonoscillation are obtained for the second-order nonlinear neutral differential equation

(∗)     

Existence and multiplicity results for periodic solutions of nonlinear difference equations

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second-order and first-order difference equations. We obtain, in particular upper and lower solutions theorems, Ambrosetti–Prodi type results and sharp existence conditions for nonlinearities which are bounded from below or above.     

Existence and nonexistence of blow-up boundary solutions for sublinear elliptic equations

In this paper we consider the semilinear elliptic problem Δu=a(x)f(u), u?0 in Ω, with the boundary blow-up condition u_|∂Ω=+∞, where Ω is a bounded domain in RN(N?2), a(x)∈C(Ω) may blow up on ∂Ω and f is assumed to satisfy (f₁) and (f₂) below which include the sublinear case f(u)=um, m∈(0,1). For the radial case that Ω=B (the unit ball) and a(x) is radial, we show that a solution exists if and only if . For Ω a general domain, we obtain an optimal nonexistence result. The existence for nonradial solutions is also studied by using sub-supersolution method.