# Existence of solutions for second-order differential equations and systems on infinite intervals

## Abstract

We study the existence of nontrivial solutions to the boundary value problem

$$-u^{\prime \prime}+cu\prime+\lambda u$$ $$=f(x,u),\ \ -\infty<x<+\infty$$

$$u(-\infty)=u(+\infty)=0$$

and to the system

$$-u^{\prime \prime}+c_{1}u^{\prime}+\lambda_{1}u$$ $$=f\left( x,u,v\right),\ \ \ \ -\infty<x<+\infty,$$

$$v^{\prime \prime}+c_{2}v^{\prime}+\lambda_{2}v$$ $$=g\left( x,u,v\right),\ \ \ -\infty<x<+\infty,$$

$$u\left( -\infty \right)$$ $$=u\left( +\infty \right) =0,\ \ v\left(-\infty \right) =v\left( +\infty \right) =0,$$

where $$c,c_{1},c_{2} ,\lambda,\lambda_{1},\lambda_{2}$$ are real positive constants and the nonlinearities $$f$$ and $$g$$ satisfy suitable conditions. The proofs are based on fixed point theorems.

## Authors

Toufik Moussaoui
Department of Mathematics, E.N.S., P.O. Box 92, 16050 Kouba, Algiers, Algeria

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Boundary value problem; fixed point theorem.

## Paper coordinates

T. Moussaoui, R. Precup, Existence of solutions for second-order differential equations and systems on infinite intervals, Electronic Journal of Differential Equations 2009 (2009) no. 94, 1-13.

## PDF

##### Journal

Electronic Journal of Differential Equations

1072-6691