## 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

**Radu Precup**

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.

## About this paper

##### Journal

Electronic Journal of Differential Equations

##### Publisher Name

##### Print ISSN

##### Online ISSN

1072-6691

google scholar link

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