Superlinear Perturbations of the Eigenvalue Problem for the Robin Laplacian Plus an Indefinite and Unbounded Potential

被引：0

作者：

Papageorgiou, Nikolaos S. ^{[1
,2
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
]}

Repovs, Dusan D. ^{[2
,5
,6
]}

机构：

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

[2] Inst Math Phys & Mech, Ljubljana 1000, Slovenia

[3] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[4] Univ Craiova, Dept Math, Craiova 200585, Romania

[5] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia

[6] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

来源：

RESULTS IN MATHEMATICS | 2020年 / 75卷 / 03期

关键词：

Superlinear perturbation; Regularity theory; Maximum principle; Constant sign and nodal solutions; Critical groups; Indefinite potential; MULTIPLE SOLUTIONS; EQUATIONS; EXISTENCE; SIGN;

D O I：

10.1007/s00025-020-01234-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when lambda is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

引用

页数：22

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