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- Title
Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions.
- Authors
Ruikuan Liu; Ruyun Ma
- 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) = λf(t, u(t)), t ϵ (0, 1), u(0) = 0, u' (0) = μh(u(0)), u"(1) = 0, u''' (1) = μg(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.
- Subjects
ELASTICITY; NONLINEAR boundary value problems; FIXED point theory; INDEXES; CONTINUATION methods; PROOF theory
- Publication
Journal of Applied Mathematics, 2014, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2014/972135