Existence of ground state solutions for the critical case of Berestycki-Lions’ theorem

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发表日期：

2025年8月21日

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Shinji Adachi,
Tatsuya Watanabe

摘要

In this paper, we are interested in the existence of ground state solutions for the critical case of the Berestycki-Lions’ theorem. By introducing a new cut-off technique and performing a detailed asymptotic estimate, we prove the existence of a ground state solution when $N=3, 4$ $N = 3, 4$ . Our existence result for the case $N=3$ $N = 3$ covers many important cases such as the focusing cubic-quintic problem and the doubly critical problem.