On the characteristic initial-value problem for linear partial functional-differential equations of hyperbolic type

Abstract

AbstractTheorems on the Fredholm alternative and well-posedness of the characteristic initial-value problemare established, where l : C($\mathcal{D}$;ℝ) is a linear bounded operator, q ∈ L($\mathcal{D}$;ℝ), ϕ:[a,b]→ℝ, ψ:[c,d]→ℝ are absolutely continuous functions and $\mathcal{D}$=[a,b]×[c,d]. Some solvability conditions of the problem considered are also given.