Existence of Nontrivial Solutions to a Critical Kirchhoff Equation With a Logarithmic‐Type Perturbation in Dimension Four
Qian Zhang, Yuzhu Han
Source abstract
ABSTRACT This paper is concerned with the existence of solutions to a critical Kirchhoff equation with a logarithmic‐type subcritical term in a bounded domain in . Under suitable assumptions on the parameters, we establish the existence of both a positive local minimum solution and a positive ground state solution. Furthermore, by a technical argument, we prove that the local minimum solution is also a ground state solution without additional assumptions. Interestingly, the results show that the introduction of the nonlocal term enlarges the ranges of the parameters such that the problem admits weak solutions, which implies that the nonlocal term has a positive effect on the existence of weak solutions.
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