On solvability of boundary value problem for asymmetric differential equation depending on x ′ - Gritsans, Armands; Sadyrbaev, Felix (Mathematical Modelling and Analysis, 2013)
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.