MULTIPLICITY OF SOLUTIONS FOR RESONANT NEUMANN PROBLEMS WITH AN INDEFINITE AND UNBOUNDED POTENTIAL

被引：0

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

[3] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 12期

关键词：

Indefinite and unbounded potential; reduction method; resonance; unique continuation property; regularity; critical groups; SEMILINEAR ELLIPTIC-EQUATIONS; ORDERED HILBERT-SPACES; NONTRIVIAL SOLUTIONS; EXISTENCE; POINTS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Caratheodory function which exhibits linear growth near +/-infinity. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (the Lyapunov-Schmidt method).

引用

页码：8723 / 8756

页数：34

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