Orlicz-Sobolev versus Holder local minimizer and multiplicity results for quasilinear elliptic equations

Abstract

We study the following boundary value problem (P)\ \ \ \ \ {-\mathrm{div}(a(|\nabla u|)\nabla u)=f(x,u),\ & in $\Omega$, u=0, & on $\partial \Omega$} with nonhomogeneous principal part. By assuming the nonlinearity $f(x,t)$ being subcritical growth, some abstract results of problem (P) are obtained: (1) Regularity; (2) Orlicz-Sobolev versus Hölder local minimizer; (3) Strong comparison principle. Applying these abstract results and critical point theory, we prove the existence of multiple solutions of problem (P) in an Orlicz-Sobolev space.

arXiv commentThis paper has been withdrawn by the author due to a crucial sign error in equation 1