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 $$\lambda $$ λ is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

中文翻译：

---

罗宾拉普拉斯算子特征值问题的超线性摄动加上一个不定无界势

我们考虑罗宾拉普拉斯算子的特征值问题的超线性扰动加上不确定和无界的势能。使用变分工具和临界群，我们证明当 $$\lambda $$ λ 接近非主特征值时，问题有七个非平凡解。我们提供其中六个的标志信息。