# Quasilinear Schrödinger equations involving critical exponents in $\mathbb{\textbf{R}}^2$

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science‎, ‎Guizhou‎ ‎Normal University‎, ‎Guiyang‎, ‎Guizhou‎, ‎550001‎, ‎P‎. ‎R‎. ‎of China.

2 School of Mathematics‎, ‎South China University of Technology‎, ‎Guangzhou‎, ‎Guangdong 510640‎, ‎P‎. ‎R‎. ‎of China.

Abstract

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $\mathbb{\textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

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Main Subjects

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### History

• Receive Date: 12 March 2015
• Revise Date: 02 September 2015
• Accept Date: 07 September 2015