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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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