NONLINEAR BIHARMONIC PROBLEMS WITH SINGULAR POTENTIALS

被引：25

作者：

Carriao, P. . C. . ^{[1
]}

Demarque, R. ^{[2
]}

Miyagaki, O. H. ^{[3
]}

机构：

[1] Univ Fed Minas Gerais, Dept Mat, BR-30161970 Belo Horizonte, MG, Brazil

[2] Univ Fed Fluminense, Dept Fis Mat, BR-28890000 Rio Ostras, RJ, Brazil

[3] Univ Fed Juiz Fora, Dept Mat, BR-36036330 Juiz De Fora, MG, Brazil

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 06期

关键词：

Biharmonic operator; critical potential; radially symmetric solution; ELLIPTIC PROBLEMS; EQUATIONS;

D O I：

10.3934/cpaa.2014.13.2141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with the problem Delta(2)u + V (vertical bar x vertical bar)u - f(u), u is an element of D-2,D-2 (R-N) where Delta(2) is biharmonic operator and the potential V > 0 is measurable, singular at the origin and may also have a continuous set of singularities. The nonlinearity is continuous and has a super-linear power-like behaviour; both sub-critical and super-critical cases are considered. We prove the existence of nontrivial radial solutions. If f is odd, we show that the problem has infinitely many radial solutions.

引用

页码：2141 / 2154

页数：14

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