Ground states to a quasilinear Schrödinger equation with Berestycki-Lions type nonlinearities

2025/05/04 by Xianyong Yang, Yang, Xianyong, Jia Yue +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2505.02141

Abstract

In this paper, we study the following quasilinear Schrödinger equation: \ - Δu - (κ)/(2)Δ( u²) u = h( u) in ℝ^N,
u ∈ H¹( ℝ^N),. where N ≥ 3,κ> 0 is a parameter, and h satisfies Berestycki-Lions condition. By using a critical point theory on a topological manifold, we obtain the existence of a ground state for N ≥ 3, a nonradial ground state for N ≥ 4, and infinitely many nonradial solutions for N = 4 or N ≥ 6. Our results generalize several classical works into quasilinear equations.

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