Multiplicity of solutions for \(p\)-Laplacian type elliptic problems with electromagnetic fields and critical nonlinearity. (English) Zbl 1371.35137

Zhang, Zhongyi

Topol. Methods Nonlinear Anal. 48, No. 1, 115-129 (2016).

Summary: We consider a class of \(p\)-Laplacian type elliptic problems with electromagnetic fields and critical nonlinearity in bounded domains. New results about the existence and multiplicity of solutions to these problems are obtained by using the concentration-compactness principle and variational method.

MSC:

35J92

Quasilinear elliptic equations with \(p\)-Laplacian

Keywords:

\(p\)-Laplacian; critical nonlinearity; electromagnetic fields