Existence and asymptotic behaviour of solutions for a quasi-linear\n schrodinger-poisson system under a critical nonlinearity

2017/07/17 by Giovany M. Figueiredo, Figueiredo, Giovany M., Gaetano Siciliano +1 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1707.05353

Abstract

In this paper we consider the following quasilinear Schr "odinger-Poisson\nsystem
left
\-
Delta u +u+
phi u =
lambda\nf(x,u)+|u|^2^*-2u · amp;

mboxin
mathbbR³

-
Delta
phi\n-
varepsilon⁴
Delta₄
phi = u² · amp;

mboxin
mathbbR³,\n
n
right. depending on the two parameters \λ,\ε>0.\n We first prove that, for \λ larger then a certain \λ^*>0,\nthere exists a solution for every \ε>0. Later, we study the\nasymptotic behaviour of these solutions whenever \ε tends to zero,\nand we prove that they converge to the solution of the Schr "odinger-Poisson\nsystem associated.\n

Cited by

• Quasilinear Schrödinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic of solutions

Related

• Quasilinear Schrödinger-Poisson system under an exponential critical nonlinearity: existence and asymptotic of solutions
• Existence and concentration of semiclassical bound states for a quasilinear Schrödinger-Poisson system
• Existence of normalized solutions for the planar Schrödinger-Poisson system with exponential critical nonlinearity
• Schrödinger-Poisson systems with a general critical nonlinearity
• Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term