Existence and multiplicity of normalized solutions for (2,q)-Laplacian equations with generic double-behaviour nonlinearities

2024/10/19 by Rui Ding, Chao Ji, Ding, Rui +3
Mathematics · #35A15 #35B09 #35B38 #35J9 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2410.15066

openalex publication_date 2024/10/19 · openalex created_date 2024/11/06 · openalex updated_date 2026/07/28

Abstract

In this paper, we study existence and multiplicity of normalized solutions for the following (2, q)-Laplacian equation \-Δu-Δ_q u+λu=f(u) x ∈ ℝ^N , ∫_ℝ^Nu² d x=c²,. where 10 is a constant. The nonlinearity f:ℝ→ ℝ is continuous, with mass-subcritical growth at the origin, mass-supercritical growth at infinity, and is more general than the sum of two powers. Under different assumptions, we prove the existence of a locally least-energy solution and the existence of a second solution with higher energy.

Related

• Normalized solutions to a class of (2, q)-Laplacian equationsin the strongly sublinear regime
• Normalized solutions to a class of (2,q)-Laplacian equations
• Normalized Solutions for the (2,q)-Laplacian Operator Between Mass-Critical Exponents
• Existence and dynamics of normalized solutions to Schrödinger equations with generic double-behaviour nonlinearities
• Multiplicity of normalized solutions for a Schrödinger equation with critical growth in ℝ^N