## Abstract

Consider the boundary value problem-(pu')'+qu=au^{+}-ßu^{-},in(0, p),c_{00}u(0)+c_{01}u'(0)=0,c_{10}u(p)+c_{11}u'(p)=0, where u^{±}=max{±u, 0}. The set of points (a, ß)?R^{2} for which this problem has a non-trivial solution is called the Fucik spectrum. When p=1, q=0, and either Dirichlet or periodic boundary conditions are imposed, the Fucik spectrum is known explicitly and consists of a countable collection of curves, with certain geometric properties. In this paper we show that similar properties hold for the general problem above, and also for a further generalization of the Fucik spectrum. We also discuss some spectral type properties of a positively homogeneous, "half-linear" problem and use these results to consider the solvability of a nonlinear problem with jumping nonlinearities. © 2000 Academic Press.

Original language | English |
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Pages (from-to) | 87-109 |

Number of pages | 23 |

Journal | Journal of Differential Equations |

Volume | 161 |

Issue number | 1 |

DOIs | |

Publication status | Published - 10 Feb 2000 |