Geodesic
Existence of weak solutions for quasilinear elliptic equations involving the $p$-Laplacian
Electronic Journal of Differential Equations, Tome 2008 (2008).

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

Summary: This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation $$ -\big(\Delta_p u +\Delta_p (u^2)\big) +V(x)|u|^{p-2}u= h(u) $$ in $\mathbb{R}^N$. Here $V$ is a positive continuous potential bounded away from zero and $h(u)$ is a nonlinear term of subcritical type. Using minimax methods, we show the existence of a nontrivial solution in $C^{1,\alpha}_{\hbox{loc}}(\mathbb{R}^N)$ and then show that it decays to zero at infinity when $1$.
Classification : 35J20, 35J60, 35Q55
Keywords: quasilinear Schrödinger equation, solitary waves, p-Laplacian, variational method, mountain-pass theorem 
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     author = {Severo, Uberlandio},
     title = {Existence of weak solutions for quasilinear elliptic equations involving the $p${-Laplacian}},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a34/}
}
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Severo, Uberlandio. Existence of weak solutions for quasilinear elliptic equations involving the $p$-Laplacian. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a34/