RESONANT ROBIN PROBLEMS WITH INDEFINITE AND UNBOUNDED POTENTIAL

被引：0

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Smyrlis, George ^{[1
]}

机构：

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

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2017年 / 49卷 / 01期

关键词：

Indefinite and unbounded potential; resonance; Robin boundary condition; maximum principle; critical groups; multiple solutions; SEMILINEAR ELLIPTIC-EQUATIONS; MULTIPLE SOLUTIONS; NEUMANN PROBLEMS; EIGENVALUES; SYMMETRIES; EXISTENCE; SIGN;

D O I：

10.12775/TMNA.2016.062

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a semilinear Robin problem with an indefinite and unbounded potential and a reaction term which asymptotically at +/-infinity is resonant with respect to any nonprincipal nonnegative eigenvalue. We prove two multiplicity theorems producing three and four nontrivial solutions respectively. Our approach uses variational methods based on the critical point theory, truncation and perturbation techniques, and Morse theory (critical groups).

引用

页码：51 / 74

页数：24

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