Multiple Solutions for a Class of New p ( x )-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions

Bei-Lei Zhang, Bin Ge and Xiao-Feng Cao
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Bei-Lei Zhang: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
Bin Ge: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
Xiao-Feng Cao: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

Mathematics, 2020, vol. 8, issue 11, 1-13

Abstract: In this paper, we consider a nonlocal p ( x ) -Kirchhoff problem with a p + -superlinear subcritical Caratheodory reaction term, which does not satisfy the Ambrosetti–Rabinowitz condition. Under some certain assumptions, we prove the existence of nontrivial solutions and many solutions. Our results are an improvement and generalization of the corresponding results obtained by Hamdani et al. (2020).

Keywords: variable exponent; nonlocal Kirchhoff equation; variational method; existence of nontrivial solutions; multiple solutions; fountain theorem; dual fountain theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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