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

Shinji Adachi () and Tatsuya Watanabe ()
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Shinji Adachi: Shizuoka University
Tatsuya Watanabe: Kyoto Sangyo University

Partial Differential Equations and Applications, 2025, vol. 6, issue 5, 1-26

Abstract: Abstract 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.

Keywords: Nonlinear elliptic equation; Ground state solution; Variational method; Sobolev critical exponent; 35J20; 35A15; 35Q55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00345-y

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