Document Type
Article
Publication Date
6-30-2023
Published In
Electronic Journal Of Differential Equations
Abstract
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, m ∈ L∞(Ω), σ, ρ ∈ L∞(∂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.
Keywords
Fucik Spectrum, resonance, nonlinear boundary condition
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Nsoki Mavinga, Q. A. Morris, and S. B. Robinson.
(2023).
"Fucik Spectrum With Weights And Existence Of Solutions For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions".
Electronic Journal Of Differential Equations.
Volume 3,
Issue Special Issue 2.
209-230.
DOI: 10.58997/ejde.sp.02.m2
https://works.swarthmore.edu/fac-math-stat/291
Comments
This work is freely available under a Creative Commons license.