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

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.

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Journal

Electronic Journal of Differential Equations

Publisher Name
Print ISSN
Online ISSN

1072-6691

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