@ARTICLE{10.21494/ISTE.OP.2023.0935,
TITLE={Bifurcation beyond the principal eigenvalues for Neumann problems with indefinite weights},
AUTHOR={Marta Calanchi, Bernhard Ruf, },
JOURNAL={Advances in Pure and Applied Mathematics},
VOLUME={14},
NUMBER={Issue 2 (Special CSMT 2022)},
YEAR={2023},
URL={https://www.openscience.fr/Bifurcation-beyond-the-principal-eigenvalues-for-Neumann-problems-with-indefi},
DOI={10.21494/ISTE.OP.2023.0935},
ISSN={1869-6090},
ABSTRACT={This paper is devoted to the study of the effects of indefinite weights on the following nonlinear Neumann problems
$$$
{(P^\pm)}
\begin{cases}
-\Delta u &= \lambda \, a(x) u \pm |u|^{p-1}u\ &\quad \hbox{in } \Omega \subset ℝ^N \\ \frac{\partial u}{\partial \nu} &=\ 0 \ & \hbox{on } \partial \Omega
\end{cases}$$$
The function $$$ a = a(x)$$$ is assumed to be continuous and sign-changing. Then the linear part has two sequences of eigenvalues. Our results establish a relation between the position of the parameter $$$\lambda$$$ and the number of nontrivial classical solutions of these problems. The proof combines spectral analysis tools, variational methods and the Clark multiplicity theorem.}}