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2002 Some remarks about the Fucik spectrum and application to equations with jumping nonlinearities
Chakib Abchir
Differential Integral Equations 15(9): 1045-1060 (2002).

Abstract

Let $L$ be a selfadjoint operator with compact resolvent and $\lambda $ an eigenvalue of $L$. When $\lambda $ is simple, it is well known that the Fucik spectrum $\Sigma $ near $\lambda $ consists of two nonincreasing curves. In this paper, we show that when $\lambda $ is not simple, $\Sigma $ contains two nonincreasing curves such that all points above or under both curves are not in $\Sigma $. After that, we give some existence results of solutions of the equation $Lu=\alpha u^{+}-\beta u^{-}+g(.,u)$ where $u^{\pm }=\max (0,\pm u)$.

Citation

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Chakib Abchir. "Some remarks about the Fucik spectrum and application to equations with jumping nonlinearities." Differential Integral Equations 15 (9) 1045 - 1060, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1022.35032
MathSciNet: MR1919761

Subjects:
Primary: 35P30
Secondary: 35J60, 35J65, 47J10

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 9 • 2002
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