Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions. (19th March 2014)

• Record Type: Journal Article
• Authors: Liu, Ruikuan; Ma, Ruyun
• Other Names: Tsitouras Ch. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-03-19
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/972135
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditions u ′′′′ ( t ) = λ f ( t, u ( t ) ), t ∈ ( 0, 1 ), u ( 0 ) = 0, u ′ ( 0 ) = μ h ( u ( 0 ) ), u ′′ ( 1 ) = 0, u ′′′ ( 1 ) = μ g ( u ( 1 ) ), where λ > 0, μ ≥ 0 are parameters, and f : 0, 1 × 0, + ∞ → 0, + ∞, h : 0, + ∞ → 0, + ∞, and g : 0, + ∞ → - ∞, 0 are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution for λ, μ sufficiently small and has no positive solution for λ large enough.