Existence of ground state sign-changing solutions for a class of quasilinear scalar field equations originating from nonlinear optics
Year: 2024
Type: article
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 [J. Differ. Equations 261, 2384–2402 (2016)] and a quantitative deformation lemma with Miranda theorem, we obtain that the problem has at least one ground state solution and one ground state sign-changing solution with two precise nodal domains and we present the concrete lower bounds of ground state solution and ground state energy. We also obtain that any weak solution of the problem has C1,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.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0215607
Authors: Xingyong Zhang, Xiaoli Yu
Institution: Kunming University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404182707