NON-EVEN LEAST ENERGY SOLUTIONS OF THE EMDEN-FOWLER EQUATION

被引：15

作者：

Kajikiya, Ryuji ^{[1
]}

机构：

[1] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 04期

基金：

日本学术振兴会;

关键词：

Emden-Fowler equation; least energy solution; non-even positive solution; variational method; SUBLINEAR ELLIPTIC-EQUATIONS; HENON EQUATION; GROUND-STATES; ASYMPTOTIC PROFILE; UNIQUENESS; GROWTH;

D O I：

10.1090/S0002-9939-2011-11172-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Emden-Fowler equation whose coefficient is even in the interval (-1,1) under the Dirichlet boundary condition. We prove that if the density of the coefficient function is thin in the interior of (-1,1) and thick on the boundary, then a least energy solution is not even. Therefore the equation has at least three positive solutions: the first one is even, the second one is a non-even least energy solution u(t) and the third one is the reflection u(t).

引用

页码：1353 / 1362

页数：10

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