Infinitely Many Solutions for Schrödinger-Choquard Equation with Critical Exponential Growth in ℝN

In this work, we study the existence of infinitely many nonnegative solutions for Schrödinger-Choquard equation @@ where Δ N is the N −Laplacian operator, h ( u ) is odd and continuous function behaving likes exp ( α 0 | u | N N − 1 ) when | u | → ∞ and N > 2 β > 1. The potential V ∈ C ( ℝ N )...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2022, Vol.28 (4), p.951-970
Main Authors: Song, Hongxue, Chen, Caisheng
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Continuity (mathematics)
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Mountains
Operators (mathematics)
Systems Theory
Vibration
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Summary:In this work, we study the existence of infinitely many nonnegative solutions for Schrödinger-Choquard equation @@ where Δ N is the N −Laplacian operator, h ( u ) is odd and continuous function behaving likes exp ( α 0 | u | N N − 1 ) when | u | → ∞ and N > 2 β > 1. The potential V ∈ C ( ℝ N ) is positive and bounded in ℝ N . Using the Schwarz symmetrization with some special techniques and symmetric mountain pass lemma, we prove the existence of infinitely many solutions for (0.1) in W 1 , N ( ℝ N ) .
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-021-09559-w