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Positive solutions of semipositone higher-order differential equations on time scales

✍ Scribed by Liang-Gen Hu; Xian-Feng Zhou

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
261 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we are concerned with the following 2nth-order differential equations on time scales

are continuous, or g is singular at t = a and/or t = b. We obtain some properties and sharp estimates of the corresponding Green's function and investigate the existence of positive solutions of the semipositone problems for 2n-order differential equations by the use of the property of Green's function, variable transformation and the fixed point index theorem.

πŸ“œ SIMILAR VOLUMES

Higher order semipositone multi-point bo
Higher order semipositone multi-point boundary value problems on time scales
✍ Abdulkadir Dogan; John R. Graef; Lingju Kong πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 347 KB

The authors obtain some existence criteria for positive solutions of a higher order semipositone multi-point boundary value problem on a time scale. Applications to some special problems are also discussed. This work extends and complements many results in the literature on this topic.

Positive solutions of a higher order neu
Positive solutions of a higher order neutral differential equation
✍ John R. Graef; Chuanxi Qian; Bo Yang πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 120 KB

## Abstract In this paper, we consider the higher order neutral delay differential equation where __p__ : [0, ∞) β†’ (0, ∞) is a continuous function, __r__ > 0 and __Οƒ__ > 0 are constants, and __n__ > 0 is an odd integer. A positive solution __x__(__t__) of Eq. (\*) is called a Class–I solution if _