Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential

2024/07/14 by Gou, Tianxiang, Radulescu, Vicentiu D.
#35A02 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.10126

Abstract

In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential (-Δ)^s u+ (ω+|x|²) u=|u|^p-2u in \Rⁿ, where n ≥ 1, 0-λ_1,s, 20 is the lowest eigenvalue of the operator (-Δ)^s + |x|². This solves an open question raised in \citeSS concerning the uniqueness of solutions to the equation.

Related

• Uniqueness of ground states to fractional nonlinear elliptic equations with harmonic potential
• Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in R^N involving fractional Laplacian
• Positive solutions for semilinear fractional elliptic problems involving\n an inverse fractional operator
• Uniqueness of Positive Solutions for Fractional Schrödinger Equations with General Nonlinearities
• A critical nonlinear fractional elliptic equation with saddle-like potentical in ℝ^N