GROUND STATE SOLUTIONS FOR A SEMILINEAR PROBLEM WITH CRITICAL EXPONENT

ANDRZEJ SZULKIN; TOBIAS WETH; MICHEL WILLEM

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GROUND STATE SOLUTIONS FOR A SEMILINEAR PROBLEM WITH CRITICAL EXPONENT

机译：具有临界指数的半线性问题的基态解

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This work is devoted to the existence and qualitative properties of ground state solutions of the Dirchlet problem for the semilinear equation -Δu - λu = |u|~(2*-2)u in a bounded domain. Here, 2~* is the critical Sobolev exponent, and the term ground state refers to minimiz_ers of the corresponding energy within the set of nontrivial solutions. We focus on the indefinite case where λ is larger than the first Dirich_let eigenvalue of the Laplacian, and we present a particularly simple approach to the study of ground states.

机译：这项工作致力于有界域中半线性方程-Δu-λu= | u |〜（2 * -2）u的Dirchlet问题基态解的存在性和定性性质。在这里，2 *是临界的Sobolev指数，术语基态指的是非平凡解集内相应能量的最小值。我们关注的是λ大于Laplacian的第一个Dirich_let特征值的不确定情况，并且我们提出了一种特别简单的方法来研究基态。

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来源
《Differential and integral equations》 |2009年第10期|共14页
作者
ANDRZEJ SZULKIN; TOBIAS WETH; MICHEL WILLEM;
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原文格式 PDF
正文语种 eng
中图分类 513B0075;
关键词
GROUND STATE; CRITICAL EXPONENT; ground state;

机译：地面状态;临界指数;地面状态;

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专利

1. GROUND STATE SOLUTIONS FOR A SEMILINEAR PROBLEM WITH CRITICAL EXPONENT [J] . ANDRZEJ SZULKIN, TOBIAS WETH, MICHEL WILLEM Differential and integral equations . 2009,第9a10期

机译：具有临界指数的半线性问题的基态解
2. POSITIVE GROUND STATE SOLUTIONS FOR FRACTIONAL LAPLACIAN SYSTEM WITH ONE CRITICAL EXPONENT AND ONE SUBCRITICAL EXPONENT [J] . Zhen Maoding, He Jinchun, Xu Haoyuan, Discrete and continuous dynamical systems . 2019,第11期

机译：具有一临界指数和一子临界指数的分数阶拉普拉斯系统的正态解
3. The Existence of Positive Solution for Semilinear Elliptic Equations with Multiple an Inverse Square Potential and Hardy-Sobolev Critical Exponents [J] . M. Khiddi Abstract and applied analysis . 2019,第16期

机译：具有多个逆平面潜力和Hardy-SoboLev临界指数的半线性椭圆方程正解的存在
4. A remark on self-similar solutions for a semilinear heat equation with critical Sobolev exponent [C] . Yūki Naito MSJ-SI International Conference "Nonlinear Dynamics in Partial Differential Equations" . 2015

机译：关于具有临界SoboLev指数的半线性热方程的自我类似解决方案的备注
5. Solutions to a nonlinear heat equation with critical exponent. [D] . Celik, Canan. 2001

机译：具有临界指数的非线性热方程的解。
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. Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation [O] . Costa, David G., Girão, Pedro M. 2014

机译：Neumann系统最小能量解的存在性和不存在性具有临界sobolev指数和半群的半线性椭圆方程的问题一个关键的低阶扰动

GROUND STATE SOLUTIONS FOR A SEMILINEAR PROBLEM WITH CRITICAL EXPONENT

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