Existence of solutions for quasilinear elliptic equations with superlinear nonlinearities
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
Boundary Value Problems 2012, 2012:90 doi:10.1186/1687-2770-2012-90Published: 10 August 2012
Working in a weighted Sobolev space, a new result involving superlinear nonlinearities for a quasilinear elliptic boundary value problem in a domain in is established. The proofs rely on the Galerkin method, Brouwer’s theorem and a new weighted compact Sobolev-type embedding theorem due to V.L. Shapiro.
MSC: 35J25, 35J62, 65L60.