On the existence of positive solutions of some nonlocal elliptic problems involving fractional p–Laplacian operator

Authors

  • Omar Djidel
  • Med-Salem Rezaoui

DOI:

https://doi.org/10.54021/seesv5n1-055

Keywords:

fractional p-Laplacian, fixed-point theorems, variational method, existence, weak solution

Abstract

Our aim in this paper is to analyze the existence of solutions to a nonlocal elliptic problem involving the fractional Laplacian operator. These operators are utilized to solve an equation defined within a bounded domain  in . The operator  is a fractional Laplacian , where  with the condition  and  is a non-negative function almost everywhere with respect to the variable , and  are real numbers. The article establishes two existence theorems for weak solutions using Tychonoff and Schauder fixed-point theorems. These theorems are formulated based on different hypotheses regarding the parameters and .

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Published

2024-04-08

How to Cite

Djidel, O., & Rezaoui, M.-S. (2024). On the existence of positive solutions of some nonlocal elliptic problems involving fractional p–Laplacian operator. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 1057–1077. https://doi.org/10.54021/seesv5n1-055