SINGULAR THIRD-ORDER m-POINT BOUNDARY VALUE PROBLEMS

AI-LING SHI; HAI-E ZHANG; JIAN-PING SUN

Title	SINGULAR THIRD-ORDER m-POINT BOUNDARY VALUE PROBLEMS
Publication Type	Journal Article
Year of Publication	2008
Authors	SHI, AI-LING, ZHANG, HAI-E, SUN, JIAN-PING
Volume	12
Issue	3
Start Page	353
Pagination	12
Date Published	2008
ISSN	1083-2564
AMS	34B10, 34B16
Abstract	This paper is concerned with the following third-order m-point boundary value problem $${ \left\{ \begin{array} \ u′′′(t)=f(t, u (t), u′(t), u′′(t))+ e (t), \ 0 < t < 1, \\ u(0) = \sum_{i=1}^{m−2} k_iu (ξ_i), u′ (0) = u′(1) = 0, \end{array} \right. }$$ where ${ f : (0, 1) × R^3 → R }$ is a function satisfying Carathéodory’s conditions, ${ e:(0, 1) → R \ and \ t(1 − t) e (t) ∈ L^1 [0, 1], 0 < ξ_1 < ξ_2 < · · · < ξ_{m−2} < 1, k_i ∈ R (i = 1, 2, . . . , m − 2) \ and }$ ${ \sum_{i=1}^{m−2} k_i \neq 1.}$ Some existence criteria of at least one solution are established by using the well-known Leray-Schauder Continuation Principle.
URL	http://www.acadsol.eu/en/articles/12/3/9.pdf
Refereed Designation	Refereed
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