Abstract
The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form , β(x) = 0, where fj satisfy local Carathéodory conditions on some [0, T] × 𝒟j ⊂ ℝ2, fj are either regular or have singularities in their phase variables (j = 1, 2, 3), Fi : 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.
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