The existence of nontrivial solution for biharmonic equation with sign-changing potential

被引：5

作者：

Su, Yu ^{[1
,2
]}

Chen, Haibo ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830054, Xinjiang, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 16期

基金：

中国国家自然科学基金;

关键词：

biharmonic equation; bipolar Rellich inequality; sign-changing potential; SCHRODINGER-POISSON SYSTEMS; 4TH-ORDER ELLIPTIC-EQUATIONS; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; MULTIPLICITY; OSCILLATIONS;

D O I：

10.1002/mma.5127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following biharmonic equation: {Delta(2)u + V lambda(x)u = alpha(x) f(u) + nu K(x)vertical bar u vertical bar(q-2) u in R-N, u is an element of H-2(R-N), (B-nu) where N >= 5, nu is an element of(0, nu(0)], 1 < q < 2, Delta(2)u = Delta(Delta u) and V lambda(x) = lambda a(x) - b(x) with lambda > 0. Firstly, we prove the bipolar Rellich inequality. Secondly, by using bipolar Rellich inequality, Gigliardo-Nirenberg inequality, and Ekeland variational principle, we prove the existence of nontrivial solution for problem B-nu.

引用

页码：6170 / 6183

页数：14

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