ON STABLE SOLUTIONS OF THE BIHARMONIC PROBLEM WITH POLYNOMIAL GROWTH

被引：29

作者：

Hajlaoui, Hatem ^{[1
]}

Harrabi, Abdellaziz ^{[1
]}

Ye, Dong ^{[2
]}

机构：

[1] Inst Math Appl & Informat, Kairouan 3100, Tunisia

[2] Univ Lorraine, IECL, UMR 7502, F-57045 Metz, France

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2014年 / 270卷 / 01期

关键词：

stable solutions; biharmonic equations; polynomial growths; NONLINEAR EIGENVALUE PROBLEMS; CLASSIFICATION; EQUATION; REGULARITY; STABILITY;

D O I：

10.2140/pjm.2014.270.79

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the nonexistence of smooth stable solutions to the biharmonic problem Delta(2)u = u(p), u > 0 in R-N for 1 < p < infinity and N < 2(1 + x(0)), where x(0) is the largest root of the equation x(4) -32 p(p+1)/(p-1)(2) x(2) + 32p (p+1) (p+3)/(p-1)(3)x -64p(p+1)(2)/(p-1)(4) = 0 In particular, as x(0) > 5 when p > 1, we obtain the nonexistence of smooth stable solutions for any N <= 12 and p > 1. Moreover, we consider also the corresponding problem in the half-space R-+(N) , and the elliptic problem Delta(2)u = lambda (u + 1)(p) on a bounded smooth domain Omega with the Navier boundary conditions. We prove the regularity of the extremal solution in lower dimensions.

引用

页码：79 / 93

页数：15

共 19 条

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[2]

Cowan C., 2013, NONLINEARITY, V26, P2357

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