POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT

Yinbin Deng; Wentao Huang

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POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT

机译：具有临界指数的拟线性椭圆型方程的正基态解。

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摘要

In this paper, we study the following quasilinear elliptic equation with critical Sobolev exponent: - △u + V(x)u - [△(1 + u~2)~(1/2)] u/(2(1+u~2)~(1/2)) = |u|~(2* -2) u + |u|~(p-2)u, x ∈R~N, which models the self-channeling of a high-power ultra short laser in matter, where N ≥ 3, 2 < p < 2~* = (2N)/(N - 2) and V(x) is a given positive potential. Combining the change of variables and an abstract result developed by Jeanjean in [14], we obtain the existence of positive ground state solutions for the given problem.

机译：本文研究具有临界Sobolev指数的以下拟线性椭圆方程：-△u + V（x）u-[△（1 + u〜2）〜（1/2）] u /（2（1 + u）〜2）〜（1/2））= | u |〜（2 * -2）u + | u |〜（p-2）u，x∈R〜N，它模拟了一个高功率超短激光物质，其中N≥3、2 <2〜* =（2N）/（N-2）和V（x）是给定的正电势。结合变量的变化和让让（Jeanjean）在[14]中提出的抽象结果，我们得到了给定问题的正基态解的存在。

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来源
《Discrete and continuous dynamical systems》 |2017年第8期|4213-4230|共18页
作者
Yinbin Deng; Wentao Huang;
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作者单位

School of Mathematics and Statistics, Central China Normal University Wuhan 430079, China;

School of Mathematics and Statistics, Central China Normal University Wuhan 430079, China;

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正文语种 eng
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Ground state solutions; quasilinear elliptic equation; critical exponent;

机译：基态解决方案;拟线性椭圆方程临界指数;

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专利

1. Two positive solutions for quasilinear elliptic equations with singularity and critical exponents [J] . Yanbin Sang, Xiaorong Luo, Zongyuan Zhu Boundary value problems . 2018,第1期

机译：具有奇异性和临界指数的拟线性椭圆型方程的两个正解
2. Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities [J] . Tsing-SanHsu, Huei-LiLin Abstract and applied analysis . 2012,第3期

机译：包含临界Hardy-Sobolev指数和凹凸非线性的加权拟线性椭圆方程正解的多重性
3. Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities [J] . Tsing-SanHsu, Huei-LiLin Abstract and applied analysis . 2012,第3期

机译：包含临界Hardy-Sobolev指数和凹凸非线性的加权拟线性椭圆方程正解的多重性
4. Existence of the Positive Solutions for some Boundary Singularity Elliptic Equation with Critical Sobolev-Hardy Exponent [C] . Zhiyang Liu International Conference on Mechanical and Electronics Engineerin . 2014

机译：临界SoboLev-Hardy指数的一些边界奇异性椭圆方程的正解的存在
5. On the number of solutions of Dirichlet problems for some quasilinear elliptic equations. [D] . Koizumi, Eiko. 2004

机译：一类拟线性椭圆型方程Dirichlet问题的解数。
6. Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent [O] . Yanbin Sang, Siman Guo -1

机译：涉及临界Sobolev指数的拟线性椭圆问题的解
7. Positive ground state solutions for a quasilinear elliptic equation with critical exponent [O] . Yinbin Deng, Wentao Huang 2017

机译：临界指数的Quasilinear椭圆方程的正面状态解决方案

POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT

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