## Differential and Integral Equations

### On the Fučí k spectrum for the $p$-Laplacian

#### Abstract

We prove that the set $\big\{(\alpha,\beta)\in\mathbb R^2 :$ the problem $-\Delta_pu=\alpha (u^+)^{p-1}-\beta (u^-)^{p-1}$ in $\Omega,$ $u=0$ on $\partial\Omega$ has a nontrivial solution $\,\,\, \}$ contains infinitely many curves which exist locally in the neighbourhood of suitable eigenvalues of the p-Laplacian operator.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 7 (2001), 867-882.

Dates
First available in Project Euclid: 21 December 2012

Micheletti, Anna Maria; Pistoia, Angela. On the Fučí k spectrum for the $p$-Laplacian. Differential Integral Equations 14 (2001), no. 7, 867--882. https://projecteuclid.org/euclid.die/1356123195