Geodesic
Existence and multiplicity results for nonlinear elliptic problems in $\bbfR^N$ with an indefinite functional
Electronic Journal of Differential Equations, Tome 2002 (2002).

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

Summary: We prove the existence of a nontrivial solution for the nonlinear elliptic problem $-\Delta u=\lambda h(x)u + a(x)g(u)$ in $\mathbb{R}^N$ where $g$ is superlinear near zero and near infinity, $a(x)$ changes sign, $\lambda $ is positive, and $h(x)\geq 0$ is a weight function. For $g$ odd, we prove the existence of an infinite number of solutions.
Classification : 35J25, 35J20, 58E05
Keywords: superlinear elliptic problems, Morse index, minimax methods 
@article{EJDE_2002__2002__a49,
     author = {Costa, David G. and Guo, Yuxia and Ramos, Miguel},
     title = {Existence and multiplicity results for nonlinear elliptic problems in $\bbfR^N$ with an indefinite functional},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/}
}
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Costa, David G.; Guo, Yuxia; Ramos, Miguel. Existence and multiplicity results for nonlinear elliptic problems in $\bbfR^N$ with an indefinite functional. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/