Singular Differential Equations in Banach Spaces

Abstract

In this chapter we consider both the differential equation $$B(t){x^{(N)}}(t) = A(t,x) + f(t)$$ (0.1) with the initial conditions $${x^{(i)}}(0) = {x_i},i = 0,1,...,N - 1$$ (0.2) where the operators B(t), A(t, x) are defined in the neighbourhood of Ω = {t, x | t | ≤ ρ, ║x║ ≤ R } and act from E 1 to E 2, E 1, E 2 are Banach spaces f (t) ∈ E 2, and singular differential equations with partial derivatives in Banach spaces.