Geodesic
Solutions to perturbed eigenvalue problems of the \(p\)-Laplacian in \(\mathbb{R}^ N\)
Electronic journal of differential equations, Tome 1997 (1997)
Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem

$ -\Delta _pu=f(x,u)\quad {\rm in}\quad {\Bbb R}^N\,. $

Under the assumptions that the primitive $F(x,u)$ of $f(x,u)$ interacts only with the first eigenvalue, we look for solutions in the space $D^{1,p}({\Bbb R}^N)$. Furthermore, we assume a condition that measures how different the behavior of the function $F(x,u)$ is from that of the p-power of u.
Classification : 35A15, 35J60
Keywords: mountain pass theorem, palais-Smale condition, first eigenvalue 
@article{EJDE_1997__1997__a47,
     author = {Bezerra do \'O,  Jo\~ao Marcos},
     title = {Solutions to perturbed eigenvalue problems of the {\(p\)-Laplacian} in {\(\mathbb{R}^} {N\)}},
     journal = {Electronic journal of differential equations},
     year = {1997},
     volume = {1997},
     zbl = {0885.35030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/}
}
TY  - JOUR
AU  - Bezerra do Ó,  João Marcos
TI  - Solutions to perturbed eigenvalue problems of the \(p\)-Laplacian in \(\mathbb{R}^ N\)
JO  - Electronic journal of differential equations
PY  - 1997
VL  - 1997
UR  - http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/
LA  - en
ID  - EJDE_1997__1997__a47
ER  - 
%0 Journal Article
%A Bezerra do Ó,  João Marcos
%T Solutions to perturbed eigenvalue problems of the \(p\)-Laplacian in \(\mathbb{R}^ N\)
%J Electronic journal of differential equations
%D 1997
%V 1997
%U http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/
%G en
%F EJDE_1997__1997__a47
Bezerra do Ó,  João Marcos. Solutions to perturbed eigenvalue problems of the \(p\)-Laplacian in \(\mathbb{R}^ N\). Electronic journal of differential equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/