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.