Work

Nontrivial Solutions and Asymptotic Behavior of Variable Critical p(x)-Laplace Equations with Negative Nonlocal Kirchhoff Terms

Year: 2026

Type: article

Abstract: We study a Dirichlet problem for a p(x)-Kirchhoff equation with negative nonlocal structure and variable critical nonlinearity. The modified Kirchhoff term and variable critical exponent break Sobolev compactness and complicate Palais–Smale sequence analysis. Using a truncation argument, the mountain pass theorem and the variable exponent concentration compactness principle, we prove the existence of a nontrivial weak solution for sufficiently large λ, with the solution norm decaying to zero as λ→+∞. This extends subcritical results to the variable critical framework.

Source: Axioms

DOI: 10.3390/axioms15090638

Authors: Zhiqian He, Bianxia Yang

Institutions: Qinghai University, Northwest A&F University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China