Existence results for a class of new (p(x), q(x))-Kirchhoff problems
DOI:
https://doi.org/10.12775/TMNA.2025.065Keywords
Kirchhoff term, variable exponents, (p(x), q(x))-equations, existence result, multiplicity result, mountain pass theoremAbstract
In the present paper, we focus on a parametric Kirchhoff problem with Dirichlet boundary condition, involving a new nonlocal term which is not necessarily positive defined. Under very general assumptions on the nonlinearity, we first establish the existence of at least one nontrivial weak solution for the problem under consideration. Then, via modifying slightly the hypotheses on the reaction term, we are able also to produce a multiplicity result for our problem. In order to archive such results we make use of variational tools, like the mountain pass theorem and the symmetric mountain pass theorem.References
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