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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