Document Type


Publication Date


Published In

Electronic Journal Of Differential Equations


We consider the boundary value problem −Δu + c(x)u = αm(x)u+βm(x)u + f(x,u), x∈Ω, (∂u)/(∂η) + σ(x)u = αρ(x)u+βρ(x)u + g(x,u), x∈∂Ω, where (α,β) ∈R2, c, mL(Ω), σ, ρL(∂Ω), and the nonlinearities f and g are bounded continuous functions. We study the asymmetric (Fucik) spectrum with weights, and prove existence theorems for nonlinear perturbations of this spectrum for both the resonance and non-resonance cases. For the resonance case, we provide a sufficient condition, the so-called generalized Landesman-Lazer condition, for the solvability. The proofs are based on variational methods and rely strongly on the variational characterization of the spectrum.


Fucik Spectrum, resonance, nonlinear boundary condition

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


This work is freely available under a Creative Commons license.

Included in

Mathematics Commons