Soliton solutions for a class of quasilinear Schrödinger equations with a parameter

2013/09/18 by Alves, Claudianor O., Wang, Youjun, Shen, Yaotian · 1 citation
#35B33 #35J20 #35J60 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4606

Abstract

Using variational methods combined with perturbation arguments, we study the existence of nontrivial classical solution for the quasilinear Schrödinger equation -Δu+ V(x)u+ \fracκ2[Δ|u|²]u=l(u), x∈ℝ^N, where V:ℝ^N→ ℝ and l:ℝ → ℝ are continuous function, κ is a parameter and N≥ 3. This model has been proposed in plasma physics and nonlinear optics. As a main novelty with respect to some previous results, we are able to deal with the case κ>0.

Cited by

• Existence and concentration of nontrivial solutions for quasilinear Schrödinger equation with indefinite potential

Related

• Soliton solutions for quasilinear Schrödinger equations involving supercritical exponent in R^N
• Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in \BR^N
• Solutions for a class of quasilinear Schrödinger equations with critical exponents term
• Existence and concentration of nontrivial solutions for quasilinear Schrödinger equation with indefinite potential
• Standing wave solutions of a quasilinear Schrödinger equation in the small frequency limit