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Characteristic of solutions for non‐local fractional p ( x ) ‐Laplacian with multi‐valued nonlinear perturbations
Author(s) -
Cheng Yi,
O'Regan Donal
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900315
Subject(s) - mathematics , compact space , nonlinear system , mathematical analysis , space (punctuation) , dirichlet boundary condition , solution set , differential inclusion , relaxation (psychology) , homogeneous , boundary (topology) , pure mathematics , set (abstract data type) , combinatorics , physics , quantum mechanics , psychology , social psychology , linguistics , philosophy , computer science , programming language
In this paper, we establish a new abstract functional spaceX K , 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.