Abstract The aim of this paper is to establish the existence of at least three distinct weak solutions for a class of nonlinear elliptic problems with double phase structure under anisotropic Neumann-type boundary conditions. The problem is formulated in the framework of anisotropic Sobolev spaces and is governed by the following system: − ∑ j = 1 N ∂ ∂ x j a j x , ∂ φ ∂ x j + b j x , ∂ φ ∂ x j + α ( x ) | φ | p 0 ( x ) − 2 φ + | φ | q 0 ( x )
Ahmed et al. (Thu,) studied this question.