NONRADIAL LEAST ENERGY SOLUTIONS OF THE p-LAPLACE ELLIPTIC EQUATIONS

Ryuji Kajikiya

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NONRADIAL LEAST ENERGY SOLUTIONS OF THE p-LAPLACE ELLIPTIC EQUATIONS

机译：p-Laplace椭圆型方程的非径向最小能量解

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摘要

We study the p-Laplace elliptic equations in the unit ball under the Dirichlet boundary condition. We call u a least energy solution if it is a minimizer of the Lagrangian functional on the Nehari manifold. A least energy solution becomes a positive solution. Assume that the nonlinear term is radial and it vanishes in |x| < a and it is positive in a < x < 1. We prove that if a is close enough to 1, then no least energy solution is radial. Therefore there exist both a positive radial solution and a positive nonradial solution.

机译：我们研究了Dirichlet边界条件下单位球中的p-Laplace椭圆方程。如果它是Nehari流形上的Lagrangian泛函的最小化子，我们称它为最小能量解。最少的能量解决方案成为肯定的解决方案。假设非线性项是径向项，并且在| x |中消失。

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来源
《Discrete and continuous dynamical systems》 |2018年第2期|547-561|共15页
作者
Ryuji Kajikiya;
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作者单位

Department of Mathematics, Faculty of Science and Engineering Saga University, Saga, 840-8502, Japan;

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正文语种 eng
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关键词
p-Laplace equation; nonradial solution; least energy solution; positive solution; variational method;

机译：p-拉普拉斯方程非径向溶液最少的能源解决方案;正解;变分法;

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1. Nonradial Solutions to Critical Elliptic Equations of Caffarelli–Kohn–Nirenberg Type [J] . Monica Musso1 and Juncheng Wei2⇓ International Mathematics Research Notices . 2012,第18期

机译：Caffarelli–Kohn–Nirenberg型临界椭圆方程的非径向解
2. Nonradial Entire Large Solutions of Semilinear Elliptic Equations [J] . LAIR Alan V 偏微分方程：英文版 . 2010,第004期

机译：半线性椭圆型方程的非径向整体大解
3. NONRADIAL POSITIVE SOLUTIONS TO SINGULAR QUASILINEAR ELLIPTIC EQUATIONS IN THE PLANE [J] . Jiongqi Wu 微分方程年刊：英文版 . 2009,第002期

机译：平面上奇异线性椭圆型方程的非径向正解。
4. OPTIMIZATION PROBLEMS FOR THE ENERGY INTEGRAL OF P-LAPLACE EQUATIONS [C] . Antonio Greco, Giovanni Porru AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：P-LAPLACE方程的能量积分优化问题
5. Topics in nonlinear elliptic equations: (1) Bifurcation theory of nonlinear elliptic equations; (2) Spike layer solutions of the Cahn-Hilliard equation. [D] . Shi, Junping. 1998

机译：非线性椭圆方程的主题：（1）非线性椭圆方程的分岔理论；（2）Cahn-Hilliard方程的尖峰层解。
6. High accuracy finite difference approximation to solutions of elliptic partial differential equations [O] . Robert E. Lynch, John R. Rice 1978

机译：椭圆型偏微分方程解的高精度有限差分近似
7. Nonradial least energy solutions of the p-Laplace elliptic equations [O] . Ryuji Kajikiya 2018

机译：p -laplace椭圆方程的非脱脂最小能量解

NONRADIAL LEAST ENERGY SOLUTIONS OF THE p-LAPLACE ELLIPTIC EQUATIONS

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