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.
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页数：22
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