@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://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.}}