General existence principles for nonlocal boundary value problems with ø-laplacian and their applications

The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (ø(x′)) ′ = f₁(t,x,x′) + f₂(t,x,x′)F ₁X + f₃(t,x,x′)f₂x,α(x) = 0, β(x) = 0, where f_j satisfy local Carathéodory conditions on some [0,T] × D_j ⊂ ℝ, f_j are either regular or have singularities in their phase variables (j = 1,2,3), f _i, : C¹[0.T] → C⁰[0,T] (i = 1,2), and α,β : C¹[0.T] → ℝ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.