A mountain pass algorithm for quasilinear boundary value problem with [formula omitted]-Laplacian

Abstract

In this paper, we deal with a specific type of quasilinear boundary value problem with Dirichlet boundary conditions and with p-Laplacian. We show two ways of proving the existence of nontrivial weak solutions. The first one uses the mountain pass theorem, the other one is based on our new minimax theorem. This method is novel even for p=2. In the paper, we also present a numerical algorithm based on the introduced approach. The suggested algorithm is illustrated on numerical examples and compared with a current approach to demonstrate its efficiency.