General existence principles for nonlocal boundary value problems with φ‐Laplacian and their applications

Ravi P. Agarwal, Donal O′Regan and Svatoslav Stanek

Abstract and Applied Analysis, 2006, vol. 2006, issue 1

Abstract: The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (φ(x′))′=f1(t,x,x′)+f2(t,x,x′)F1x+f3(t,x,x′)F2x,α(x)=0, 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.

Date: 2006
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https://doi.org/10.1155/AAA/2006/96826

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2006:y:2006:i:1:n:096826

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