Fractional elliptic obstacle systems with multivalued terms and nonlocal operators

Abstract

In this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi, qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractional elliptic obstacle system is formulated by a fully nonlinear coupled system driven by two nonlinear and nonmonotone variational inequalities with constraints. The nonemptiness and compactness of solution set in the weak sense are proved via employing a surjectivity theorem to the multivalued operators formulated by the sum of a multivalued pseudomonotone operator and a maximal monotone operator.

Keywords

• fractional (p,q)-Laplacian
• nonlocal operator
• multivalued term
• obstacle problem
• pseudomonotone operator
• existence