Multiple solutions for the p-laplace equation with nonlinear boundary conditions.

JULIAN FERNANDEZ BONDER

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

TEXAS STATE UNIVERSITY

Año: 2006 vol. 2006 p. 1 - 7

1072-6691

In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $−Delta_pu +  |u|^{p−2}u = f(x, u)$ in a smooth bounded domain of $R^N$ with nonlinear boundary conditions $| abla u|^{p−2} rac{partial u}{partial n} = g(x, u)$ on the boundary of the domain. The proof is based on variational arguments.−Delta_pu +  |u|^{p−2}u = f(x, u)$ in a smooth bounded domain of $R^N$ with nonlinear boundary conditions $| abla u|^{p−2} rac{partial u}{partial n} = g(x, u)$ on the boundary of the domain. The proof is based on variational arguments.