Soliton solutions for quasilinear Schrödinger equations involving supercritical exponent in R^N

2006/09/07 by Abbas Moameni, Moameni, Abbas
Mathematics · Physics and Astronomy · #35J10 #35J20 #35J25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0609191

openalex publication_date 2006/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of positive solutions to the quasilinear elliptic problem -εΔu+V(x)u-εk(\Del(|u|²))u=g(u), u>0, x ∈ R^N, where g has superlinear growth at infinity without any restriction from above on its growth. Mountain pass in a suitable Orlicz space is employed to establish this result. These equations contain strongly singular nonlinearities which include derivatives of the second order which make the situation more complicated. Such equations arise when one seeks for standing wave solutions for the corresponding quasilinear Schrödinger equations. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

Citations

• Existence of solitary waves in higher dimensions

Related

• Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in \BR^N
• Soliton solutions for a class of quasilinear Schrödinger equations with a parameter
• Standing wave solutions of a quasilinear Schrödinger equation in the small frequency limit
• Standing Waves for nonlinear Schrodinger Equations involving critical growth
• Existence of standing waves solution for a Nonlinear Schrödinger equations in ℝ^N