Existence of multiple positive solutions to three-point boundary value problems on time scales

We consider the three-point even order boundary value problem on time scales, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where n ≥ 1, a < b < σ(c), σ(c) is right-dense and f: [a, σ(c)] x R → R is continuous. First, we establish the existence of at least three positive solutions by usi...

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Bibliographic Details
Published inInternational journal of difference equations Vol. 4; no. 2; p. 219
Main Authors Prasad, K.R, Murali, P, Rao, S. Nageswara
Format Journal Article
LanguageEnglish
Published Research India Publications 01.12.2009
Subjects
Boundary value problems
Difference equations
Existence theorems
Fixed point theory
India
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Summary:We consider the three-point even order boundary value problem on time scales, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where n ≥ 1, a < b < σ(c), σ(c) is right-dense and f: [a, σ(c)] x R → R is continuous. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. We also establish the existence of at least 2m - 1 positive solutions for arbitrary positive integer m. AMS Subject Classifications: 39A10, 34B15, 34A40. Keywords: Time scales, boundary value problem, positive solution, cone, multiple positive solution.
ISSN:0973-6069
0974-1828