Geodesic
Existence of solutions for second-order differential equations and systems on infinite intervals
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the existence of nontrivial solutions to the boundary-value problem $$\displaylines{ -u''+cu'+\lambda u = f(x,u),\quad -\infty +\infty , \cr u(-\infty )=u(+\infty ) =0 }$$ and to the system $$\displaylines{ -u''+c_1u'+\lambda _1u = f(x,u,v),\quad -\infty +\infty , \cr -v''+c_2v'+\lambda _2v = g(x,u,v),\quad -\infty +\infty , \cr u(-\infty )=u(+\infty ) =0, \quad v(-\infty )=v(+\infty ) =0, }$$ 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.
Classification : 34B40
Keywords: boundary value problem, fixed point theorem 
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     author = {Moussaoui, Toufik and Precup, Radu},
     title = {Existence of solutions for second-order differential equations and systems on infinite intervals},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a141/}
}
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Moussaoui, Toufik; Precup, Radu. Existence of solutions for second-order differential equations and systems on infinite intervals. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a141/