The Fucik Spectrum of General Sturm–Liouville Problems

The full text article is not available for purchase.

The publisher only permits individual articles to be downloaded by subscribers.


Consider the boundary value problem-(pu′)′+qu=αu+-u-, in (0, ),c00u(0)+c01u(0)=0, c10u()+c11u′()=0,where u±=max{±u, 0}. The set of points (α)∈ℝ2 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. Copyright 2000 Academic Press.

Document Type: Research Article

Affiliations: Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland

Publication date: February 1, 2000

Related content



Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more