Geodesic
Existence and multiplicity results for nonlinear elliptic problems in \(\mathbb{R}^N\) with an indefinite functional
Electronic journal of differential equations, Tome 2002 (2002)
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 {\(\mathbb{R}^N\)} with an indefinite functional},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1008.35014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/}
}
TY  - JOUR
AU  - Costa,  David G.
AU  - Guo,  Yuxia
AU  - Ramos,  Miguel
TI  - Existence and multiplicity results for nonlinear elliptic problems in \(\mathbb{R}^N\) with an indefinite functional
JO  - Electronic journal of differential equations
PY  - 2002
VL  - 2002
UR  - http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/
LA  - en
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%A Costa,  David G.
%A Guo,  Yuxia
%A Ramos,  Miguel
%T Existence and multiplicity results for nonlinear elliptic problems in \(\mathbb{R}^N\) with an indefinite functional
%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/
%G en
%F EJDE_2002__2002__a49
Costa,  David G.; Guo,  Yuxia; Ramos,  Miguel. Existence and multiplicity results for nonlinear elliptic problems in \(\mathbb{R}^N\) with an indefinite functional. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a49/