Nonlocal Double Phase Complementarity Systems with Convection Term and mixed Boundary Conditions

In the present paper, we are concerned with the study of a nonlinear complementarity problem (NCP, for short) with a nonlinear and nonhomogeneous partial differential operator (called double phase differential operator), a convection term (i.e., a reaction depending on the gradient), a generalized multivalued boundary condition, and two nonlocal terms which appear in the domain and boundary, respectively. First, we formulate NCP to a nonlinear bilateral obstacle variational problem with feedback effect. Then, a regularized approximation problem corresponding to NCP is introduced via applying the Moreau–Yosida approximating method. By employing a surjectivity theorem to multivalued pseudomonotone operators and a limiting procedure for solutions of approximating problems, we obtain the properties of solution set to NCP, including the nonemptiness and compactness. Finally, under further assumptions, we examine several extended versions of existence theorem to NCP.