Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs. (13th July 2016)

• Record Type: Journal Article
• Authors: Sun, Jian-Ping; Yang, Xue-Mei; Zhao, Ya-Hong
• Other Names: Llorens-Fuster Enrique Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-07-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/6874643
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We are concerned with the following system of third-order three-point boundary value problems: u ′ ′ ′ ( t ) + f ( t, v ( t ) ) = 0, t ∈ ( 0, 1 ), v ′ ′ ′ ( t ) + g ( t, u ( t ) ) = 0, t ∈ ( 0, 1 ), u ( 0 ) = u ′ ′ ( 0 ) = 0, u ′ ( 1 ) = α u ( η ), v ( 0 ) = v ′ ′ ( 0 ) = 0, and v ′ ( 1 ) = α v ( η ), where 0 < η < 1 and 0 < α < 1 / η . By imposing some suitable conditions on f and g, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.