On Solvability of Boundary Value Problem for Asymmetric Differential Equation Depending on X ′

Abstract

We state the conditions of geometrical nature which guarantee the existence of a solution to the boundary value problem x ′′ + 2δx ′ + λf (x + ) − µg(x −) = h(t, x, x ′ ), x(0) = 0 = x(1) with a damping term 2δx ′ and nonnegative parameters λ, µ, provided that f (x +) − g(x −) is a sector-bounded nonlinearity.

On Solvability of the Damped Fučík Type Problem With Integral Condition

“…The spectrum of the problem (2.1) was obtained in the work [3]. The branches of the spectrum for the problem (2.1) can be obtained from the classical Fučík spectrum by translation parallel to the vector (δ 2 , δ 2 ).…”

“…for continuous and bounded h(t, x, x ) were considered in the work [3] also. The spectrum of the problem (2.1) and solvability regions for the problem (2.2) are shown in Fig.…”