TITLE

GENERAL EXISTENCE PRINCIPLES FOR NONLOCAL BOUNDARY VALUE PROBLEMS WITH Ø-LAPLACIAN AND THEIR APPLICATIONS

AUTHOR(S)
Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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.
ACCESSION #
24049419

 

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