Existence of solutions for second-order differential equations and systems on infinite intervals
Electronic journal of differential equations, Tome 2009 (2009)
We study the existence of nontrivial solutions to the boundary-value problem
and to the system
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.
| $\displaylines{ -u''+cu'+\lambda u = f(x,u),\quad -\infty +\infty , \cr u(-\infty )=u(+\infty ) =0 }$ |
| $\displaylines{ -u''+c_1u'+\lambda _1u = f(x,u,v),\quad -\infty +\infty , \cr -v''+c_2v'+\lambda _2v = g(x,u,v),\quad -\infty +\infty , \cr u(-\infty )=u(+\infty ) =0, \quad v(-\infty )=v(+\infty ) =0, }$ |
@article{EJDE_2009__2009__a141,
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},
year = {2009},
volume = {2009},
zbl = {1179.34029},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a141/}
}
TY - JOUR AU - Moussaoui, Toufik AU - Precup, Radu TI - Existence of solutions for second-order differential equations and systems on infinite intervals JO - Electronic journal of differential equations PY - 2009 VL - 2009 UR - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a141/ LA - en ID - EJDE_2009__2009__a141 ER -
%0 Journal Article %A Moussaoui, Toufik %A Precup, Radu %T Existence of solutions for second-order differential equations and systems on infinite intervals %J Electronic journal of differential equations %D 2009 %V 2009 %U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a141/ %G en %F EJDE_2009__2009__a141
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/