Existence of solutions for nonlocal Schrödinger–Kirchhoff problems with critical Trudinger–Moser nonlinearity

Jin Liang and Zhi‐Cheng Xiong

Mathematische Nachrichten, 2025, vol. 298, issue 5, 1680-1699

Abstract: In this paper, we are concerned with solutions for nonlocal Schrödinger–Kirchhoff problems with critical Trudinger–Moser nonlinearity on a bounded domain with Lipschitz boundary. With the help of the minimax method, the fractional Trudinger–Moser inequality, Ekeland's variational principle, and other techniques, we establish an existence theorem for a nonnegative solution with positive energy to a class of nonlocal Schrödinger–Kirchhoff problems and an existence theorem for a nontrivial solution with negative energy to another class of nonlocal Schrödinger–Kirchhoff problems.

Date: 2025
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https://doi.org/10.1002/mana.12013

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:5:p:1680-1699

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