Geodesic
Soliton solutions for a quasilinear Schrödinger equation
Electronic Journal of Differential Equations, Tome 2013 (2013).

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

Summary: In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\Delta_p u-\frac{p}{2^{p-1}}u\Delta_p(u^2)=f(x,u) $$ in a bounded smooth domain $\Omega\subset\mathbb{R}^{N}$ with Dirichlet boundary conditions.
Classification : 35B38, 35D05, 35J20
Keywords: quasilinear Schrödinger equation, soliton solution, critical point theorem, Fountain theorem, dual Fountain theorem 
@article{EJDE_2013__2013__a42,
     author = {Liu, Duchao},
     title = {Soliton solutions for a quasilinear {Schr\"odinger} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a42/}
}
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Liu, Duchao. Soliton solutions for a quasilinear Schrödinger equation. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a42/