we are concerned with proving the existence of positive solutions of general two point boundary value problems for the nonlinear equation k(t) := -[r(t)zA(t)lA = f(t, z(t)). We will use fixed point theorems concerning cones in a Banach space. Important results concerning Green's functions for gener
Positive solutions of singular differential equations on measure chains
β Scribed by Jin Liang; Ti-Jun Xiao; Zhao-Cai Hao
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 678 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0898-1221
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## Abstract We investigate the existence of positive solutions to the singular fractional boundary value problem: \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$^c\hspace{-1.0pt}D^{\alpha }u +f(t,u,u^{\prime },^c\hspace{-2.0pt}D^{\mu }u)=0$\end{document}, __u__β²(0) = 0
With new schemes, the existence of the positive solutions is proved to some secondorder nonlinear singular boundary value problems and initial value problems, which have higher-order singularities.
The existence of positive solutions of a second order differential equation of the form z"+ g(t) f (z)=0 (1.1) with suitable boundary conditions has proved to be important in theory and applications whether g is continuous in [0, 1] or g has singularities. These equations often arise in the study