Existence of ground state sign-changing solutions for a class of quasilinear scalar field equations originating from nonlinear optics

2023/12/25 by Xingyong Zhang, Xiaoli Yu, Zhang, Xingyong +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2312.15739

openalex publication_date 2023/12/25 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/28

Abstract

This paper is mainly concerned with the existence of ground state sign-changing solutions for a class of second order quasilinear elliptic equations in bounded domains which derived from nonlinear optics models. Combining a non-Nehari manifold method due to Tang and Cheng [31] and a quantitative deformation lemma with Miranda theorem, we obtain that the problem has at least one ground state sign-changing solution with two precise nodal domains. We also obtain that any weak solution of the problem has C^1,σ-regularity for some σ∈(0,1). With the help of Maximum Principle, we reach the conclusion that the energy of the ground state sign-changing solutions is strictly larger than twice that of the ground state solutions.

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