Abstract
AbstractWe 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 $$\lambda $$
λ
is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.
Funder
Javna Agencija za Raziskovalno Dejavnost RS
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference21 articles.
1. Castro, A., Cassio, J., Velez, C.: Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries. Annali Mat. Pura Appl. 192, 607–619 (2013)
2. D’Agui, G., Marano, S., Papageorgiou, N.S.: Multiple solutions to a Robin problem with indefinite weight and asymmetric reaction. J. Math. Anal. Appl. 433, 1821–1845 (2016)
3. Hu, S., Papageorgiou, N.S.: Semilinear Robin problems with indefinite potential and competition phenomena, Acta Appl. Math., in press (https://doi.org/10.1007/s10440-019-00284-y)
4. Marino, A., Saccon, C.: Some variational theorems of mixed type and elliptic problems with jumping nonlinearities. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 25, 631–665 (1997)
5. Mugnai, D.: Multiplicity of critical points in presence of linking: application to a superlinear boundary value problem. Nonlinear Differ. Equ. Appl. (NoDEA) 11, 379–391 (2004)
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