On Fučík type spectrum for problem with integral nonlocal boundary condition

2019

The Fučík equation x' '= -μ x+λ x- with two types of nonlocal boundary value conditions are considered. The Fučík type spectrum for both problems are constructed. The visualization of the spectrum for some values of parameter γ is provided.

Mathematical knowledge in elementary school and for future engineers

2018

ON SOLVABILITY OF THE DAMPED FUČÍK TYPE PROBLEM WITH INTEGRAL CONDITION

2014

The solvability results are established for the boundary value problem with a damping term , x(0) = 0, where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0

The Fučík spectrum for nonlocal BVP with Sturm–Liouville boundary condition

2014

Boundary value problem of the form x''=-μx++λx-, αx(0)+(1-α)x'(0)=0, ∫01 x(s)ds=0 is considered, where μ,λ∈ R and α∈ [0,1]. The explicit formulas for the spectrum of this problem are given and the spectra for some α values are constructed. Special attention is paid to the spectrum behavior at the points close to the coordinate origin.