Positive solutions of nonlinear three-point boundary-value problems

By Ruyun Ma, Haiyan Wang. 2003

126 citations recorded by the source corpus.

Abstract Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ1(t) be the unique solution of the linear boundary value problem u″(t)+a(t)u′(t)+b(t)u(t)=0, t∈(0,1), u(0)=0, u(1)=1. We study the existence of positive solutions to the nonlinear boundary-value problem u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1), u(0)=0, αu(η)=u(1), where 0 0, and f∈C([0,∞),[0,∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/53561dcf0c2530d1eff2caf313464e6344f2f438

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In Applied Mathematics

1. Zhilin Yang
2. Meiqiang Feng
3. D. Xie
4. Weigao Ge
5. Ruyun Ma
6. Xuemei Zhang
7. Gennaro Infante
8. Christopher S. Goodrich

In Numerical Analysis

1. Meiqiang Feng
2. Zhilin Yang
3. Weigao Ge
4. D. Xie
5. Ruyun Ma
6. Xuemei Zhang
7. Gennaro Infante
8. J. R. L. Webb

Citations in the corpus

• Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations (2009, background): “Since then a lot of attention has been paid to the study of nonlinear multi-point boundary value problems, see [12–17,19–31].”
• Positive solutions of a second-order integral boundary value problem (2006, background): “In [18], Ma and Wang studied the three-point boundary value problem{ u′′ + a(t)u′ + b(t)u(t) + h(t)f (u) = 0, u(0) = 0, αu(η) = u(1), (30) where a ∈ C([0,1]), b ∈ C([0,1],R−); η ∈ (0,1); and h ∈ C([0,1],R+) not vanishing identically on [0,1].”
• Positive solutions for nonlinear m-point Eigenvalue problems (2004, unknown): “We refer the readerto [4,8,9,12] for some references along t line.”
• Symmetric positive solutions for p-Laplacian fourth-order differential equations with integral boundary conditions (2008, background): “To identify a few, we refer the reader to [1–8,10,14,16–34] and references therein.”
• A Survey On Nonlocal Boundary Value Problems (2007, methodology): “In [102], they studied the existence of positive solutions of the following BVP x′′ + a(t)x′(t) + b(t)x(t) + h(t)f(x) = 0, t ∈ (0, 1), (34) x(0) = 0, x(1) = αx(η) (35) under the assumptions: (H1) h : [0, 1] → [0,∞) is continuous and h(t) 6 ≡0 on any subinterval of [0, 1]; (H2) f : [0,∞) → [0,∞) is c”
• Positive solutions for second order impulsive differential equations with integral boundary conditions (2011, unknown): “2 [9].”