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Positive Solutions for Second–Order m–Point Boundary Value Problems on Time Scales.
- Source :
-
Acta Mathematica Sinica . Oct2006, Vol. 22 Issue 6, p1797-1804. 8p. - Publication Year :
- 2006
-
Abstract
- Let $${\Bbb T}$$ be a time scale such that 0, T ∈ $${\Bbb T}$$ . By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m–point boundary value problem on time scales where a ∈ C ld ((0, T), [0,∞)), f ∈ C ld ([0,∞) × [0,∞), [0,∞)), β, γ ∈ [0,∞), ξ i ∈ (0, ρ( T)), b, a i ∈ (0,∞) (for i = 1, . . . , m− 2) are given constants satisfying some suitable hypotheses. We show that this problem has at least one positive solution for sufficiently small b > 0 and no solution for sufficiently large b. Our results are new even for the corresponding differential equation ( $${\Bbb T}$$ = ℝ) and difference equation ( $${\Bbb T}$$ = ℤ). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 22
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 22615826
- Full Text :
- https://doi.org/10.1007/s10114-005-0748-5