Potential Landesman-Lazer type conditions and the Fucik spectrum
Date
2005-08-29
Authors
Tomiczek, Petr
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We prove the existence of solutions to the nonlinear problem
u''(x) + λ+u+(x) = λ_u-(x) + g(x, u(x)) = ƒ(x), x ∈ (0, π),
u(0) = u(π) = 0
where the point [λ+, λ_] is a point of the Fučík spectrum and the nonlinearity g(x, u(x)) satisfies a potential Landesman-Lazer type condition. We use a variational method based on the organization of the Saddle Point Theorem.
Description
Keywords
Resonance, Eigenvalues, Jumping nonlinearities, Fučík spectrum
Citation
Tomiczek, P. (2005). Potential Landesman-Lazer type conditions and the Fučík spectrum. <i>Electronic Journal of Differential Equations, 2005</i>(94), pp. 1-12.
Rights
Attribution 4.0 International