Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem. (20th June 2010)

• Record Type: Journal Article
• Authors: Li Li, Yaohong Yaohong; Wei Wei, Zhongli Zhongli
• Other Names: Kiguradze Kiguradze Ivan T. Ivan T. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-06-20
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/708376
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We study the existence of multiple positive solutions for n th-order multipoint boundary value problem. u ( n ) ( t ) + a ( t ) f ( u ( t ) ) = 0, t ∈ ( 0, 1 ), u ( j - 1 ) ( 0 ) = 0 ( j = 1, 2, …, n - 1 ), u ( 1 ) = ∑ i = 1 m α i u ( η i ), where n ≥ 2, 0 < η 1 < η 2 < ⋯ < η m < 1, α i > 0, i = 1, 2, …, m . We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.