Characteristic of solutions for non‐local fractional p(x)‐Laplacian with multi‐valued nonlinear perturbations

Yi Cheng and Donal O'Regan

Mathematische Nachrichten, 2021, vol. 294, issue 7, 1311-1332

Abstract: In this paper, we establish a new abstract functional space XK,p(·)(Ω) where K is a uncertain weighted function and p is a variable exponent. Based on the properties of this space, we consider the existence and regularity of weak solutions for non‐local fractional differential inclusion with homogeneous Dirichlet boundary conditions. Under a suplinear growth condition we obtain the existence of weak solutions, the compactness and Hölder regularity of the solution set using set‐valued analysis and the surjectivity principle of pseudomonotonicity. Furthermore, the existence of extremal solutions and a relaxation result is discussed.

Date: 2021
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https://doi.org/10.1002/mana.201900315

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