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Asymmetric elliptic problems in \(\mathbb{R}^N\). (English) Zbl 1118.35024
Summary: We work on the whole \(\mathbb{R}^N\) and prove the existence of a first nonprincipal eigenvalue for an asymmetric problem with weights involving the \(p\)-Laplacian. As an application we obtain a first nontrivial curve in the corresponding Fučik spectrum.

MSC:
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
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