Existence and Multiplicity of Solutions for a Bi-Non-Local Problem

Jiabin Zuo, Tianqing An, Alessio Fiscella and Chungen Liu
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Jiabin Zuo: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Tianqing An: College of Science, Hohai University, Nanjing 210098, China
Alessio Fiscella: Dipartimento di Matematica e Applicazioni, Universita degli Studi di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy
Chungen Liu: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 12, 1-12

Abstract: The aim of this paper is to investigate the existence and multiplicity of solutions for a bi-non-local problem. Precisely, we show that the above problem admits at least a non-trivial positive energy solution by using the mountain pass theorem. Furthermore, with the help of the fountain theorem, we obtain the existence of infinitely many positive energy solutions, assuming a symmetric condition for g . The main feature and difficulty of this paper is the presence of a double non-local term involving two variable parameters.

Keywords: Kirchhoff coefficient; p (·)-fractional Laplacian; variable exponent; variable-order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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