Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 94, pp. 1-13.

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

Authors: Toufik Moussaoui (E.N.S., Algiers, Algeria)
         Radu Precup (Babes-Bolyai Univ., Cluj, Romania)

Abstract: 
 We study the existence of nontrivial solutions to the
 boundary-value problem
 $$\displaylines{
 -u''+cu'+\lambda u  =  f(x,u),\quad -\infty <x<+\infty , \cr
 u(-\infty )=u(+\infty )  =0
 }$$
 and to the system
 $$\displaylines{
 -u''+c_1u'+\lambda _1u  =  f(x,u,v),\quad
 -\infty <x<+\infty , \cr
 -v''+c_2v'+\lambda _2v  =  g(x,u,v),\quad
 -\infty <x<+\infty , \cr
 u(-\infty )=u(+\infty )  =0,   \quad
 v(-\infty )=v(+\infty )  =0,
 }$$
 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.
 
Submitted October 7, 2008. Published August 06, 2009.
Math Subject Classifications: 34B40.
Key Words: Boundary value problem; fixed point theorem.