TY  - Type of reference 
TI  - Bifurcation beyond the principal eigenvalues for Neumann problems with indefinite  weights 
AU  - Marta Calanchi 
AU  - Bernhard Ruf 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2023.0935 
JF  - Advances in Pure and Applied Mathematics 
KW  - eigenvalues,  indefinite weight,  Neumann problems,  bifurcation, eigenvalues,  indefinite weight,  Neumann problems,  bifurcation,  
L1  - https://openscience.fr/IMG/pdf/iste_apam23v14nspe_2.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/03/7 
SN  - 1869-6090 
TT  - Bifurcation au-delà des valeurs propres principales pour les problèmes de Neumann avec des poids indéfinis 
UR  - https://openscience.fr/Bifurcation-beyond-the-principal-eigenvalues-for-Neumann-problems-with-indefi 
IS  - Issue 2 (Special CSMT 2022) 
VL  - 14 
ER  -