# Multibump solutions for quasilinear elliptic equations with critical growth

@article{Liu2013MultibumpSF,
title={Multibump solutions for quasilinear elliptic equations with critical growth},
author={Jiaquan Liu and Zhi-Qiang Wang and Xian Wu},
journal={Journal of Mathematical Physics},
year={2013},
volume={54},
pages={121501}
}
• Published 3 December 2013
• Mathematics
• Journal of Mathematical Physics
The current paper is concerned with constructing multibump solutions for a class of quasilinear Schrodinger equations with critical growth. This extends the classical results of Coti Zelati and Rabinowitz [Commun. Pure Appl. Math. 45, 1217–1269 (1992)] for semilinear equations as well as recent work of Liu, Wang, and Guo [J. Funct. Anal. 262, 4040–4102 (2012)] for quasilinear problems with subcritical growth. The periodicity of the potentials is used to glue ground state solutions to construct…
14 Citations

### Periodic and asymptotically periodic quasilinear elliptic systems

• Mathematics
• 2020
In this work, we are concerned with the existence and nonexistence of ground state solutions for the following class of quasilinear Schrodinger coupled systems taking into account periodic or

### Ground state solutions for a modified fractional Schrödinger equation with critical exponent

• Mathematics
Mathematical Methods in the Applied Sciences
• 2020
In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations (−Δ)αu+μu+κ[(−Δ)αu2]u=σ|u|p−1u+|u|q−2u,x∈RN, where N≥2 , α∈(0,1) , μ , σ and κ are

### A Nontrivial Solution of a Quasilinear Elliptic Equation Via Dual Approach

• Mathematics
Acta Mathematica Scientia
• 2019
In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in ℝN which includes the so-called modified nonlinear Schrödinger equation as a special case.

### Quasilinear Schrödinger equations with nonlinearities interacting with high eigenvalues

• Mathematics
Journal of Mathematical Physics
• 2019
It is the established existence and multiplicity of solutions for quasilinear Schrodinger equations where the nonlinear term is 3-superlinear or 3-asymptotically linear at infinity in an appropriate

### Existence of solution for a generalized quasilinear elliptic problem

• Mathematics
• 2017
It establishes existence and multiplicity of solutions to the elliptic quasilinear Schrodinger equation −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=h(x,u),x∈ℝN,where g, h, V are suitable smooth functions. The

• Mathematics
• 2017

### Nash moser methods for the solution of quasilinear schrödinger equations

• Mathematics
• 1999
Using new Nash Moser techniques for Frechet spaces by M. Poppenberg the local existence, uniqueness and continuous dependence of smooth solutions of a special quasilinear evolutionary Schrodinger

### EXISTENCE OF WEAK SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN

This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation − ` ∆pu + ∆p(u ) ́ + V (x)|u|p−2u = h(u) in RN . Here V is a positive continuous potential bounded