ORIGINAL PAPER
Characteristic of solutions for non-local fractional -Laplacian with multi-valued nonlinear perturbations
Yi Cheng,
Donal O'Regan,
Corresponding Author
Yi Cheng
Department of Mathematics, Bohai University, Jinzhou, 121013 P. R. China
Correspondence
Yi Cheng, Department of Mathematics, Bohai University, Jinzhou, 121013, P. R. China.
Email: [email protected]
Search for more papers by this authorDonal O'Regan
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Search for more papers by this authorYi Cheng,
Donal O'Regan,
Corresponding Author
Yi Cheng
Department of Mathematics, Bohai University, Jinzhou, 121013 P. R. China
Correspondence
Yi Cheng, Department of Mathematics, Bohai University, Jinzhou, 121013, P. R. China.
Email: [email protected]
Search for more papers by this authorDonal O'Regan
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Search for more papers by this authorFirst published: 25 May 2021
Abstract
In this paper, we establish a new abstract functional space 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.
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