Fractional elliptic obstacle systems with multivalued terms and nonlocal operators - Cen, Jinxia; Zeng, Shengda; Bahrouni, Anouar (Nonlinear Analysis: Modelling and Control, 2024)
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; compactness