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

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