Geodesic
Solutions to perturbed eigenvalue problems of the $p$-Laplacian in $\bbfR\sp N$
Electronic Journal of Differential Equations, Tome 1997 (1997).

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

Summary: 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 $\bbfR\sp N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1997},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/}
}
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Bezerra do Ó, João Marcos. Solutions to perturbed eigenvalue problems of the $p$-Laplacian in $\bbfR\sp N$. Electronic Journal of Differential Equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a47/