Existence of Positive Solutions to a Nonlocal Boundary Value Problem with p-Laplacian onTime Scales. (28th January 2010)

• Record Type: Journal Article
• Authors: Sun, Ting-Ting; Wang, Lin-Lin; Fan, Yong-Hong
• Other Names: Eloe Paul Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2010(2010)
• Publication Date: 2010-01-28
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2010/809497
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : The nonlocal boundary value problem, withp -Laplacian of the form( Φ p ( u ▵ ) ) ▵ ( t ) + h ( t ) f ( t, u ( t ) ) = 0, t ∈ [ t 1, t m ) T, u ▵ ( t 1 ) − ∑ j = 1 n θ j u ▵ ( η j ) − ∑ i = 1 m − 2 ϵ i u ( ξ i ) = 0, u ▵ ( t m ) = 0, has been considered. Two existence criteria of at least one and three positive solutions are presented. The first one is based on the Four functionals fixed point theorem in the work of R. Avery et al. (2008), and the second one is based on the Five functionals fixed point theorem. Meanwhile an example is worked out to illustrate the main result.