Pohozaev manifold constraint for solving nonlinear Schrödinger equations with potentials vanishing at infinity

2020/06/25 by Liliane A. Maia, Maia, Liliane A., Gilberto S. Pina +3
Computer Science · Mathematics · #35J10 #35J20 #35Q40 #35Q55 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.14687

openalex publication_date 2020/06/25 · openalex created_date 2020/07/02 · openalex updated_date 2026/07/28

Abstract

Existence of a positive solution for a class of nonlinear Schrödinger equations with potentials which decay to zero at infinity, with an appropriate rate, approaching zero mass type limit scalar field equations, is established via a new composition of two translated and dilated solitons and its projection on the so called Pohozaev manifold.

Citations

• A relation between pointwise convergence of functions and convergence of functionals
• Nonlinear scalar field equations, I existence of a ground state

Related

• Positive solutions to Schrödinger equations and geometric applications
• On a "zero mass" nonlinear Schrodinger equation
• Relaxation of Solitons in Nonlinear Schrodinger Equations with Potential
• Existence of a positive solution to a nonlinear scalar field equation with zero mass at infinity
• Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity