Existence of solutions for nonlinear BVPs of second-order differential equations on measure chains

Lian, Wei-Cheng; Chou, Chin-Chen; Liu, Chieh-Ting; Wong, Fu-Hsiang

doi:10.1016/s0895-7177(01)00102-9

Cited by 10 publications

(10 citation statements)

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“…This result has been extended and developed by many authors (see Erbe, Hu and Wang [2] and Lian, Wong and Yeh [7] for some references).…”

Section: Then (12) Has At Least One Positive Solution If Eithermentioning

confidence: 63%

Existence of positive solutions for second order m-point boundary value problems

2002

Ann. Polon. Math.

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Abstract. Let α, β, γ, δ ≥ 0 and := γβ + αγ + αδ > 0. Let ψ(t) = β + αt, φ(t) = γ + δ − γt, t ∈ [0, 1]. We study the existence of positive solutions for the m-point boundary value problemWe show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and Wang for two-point BVPs and a result established by the author for three-point BVPs.1. Introduction. The study of multi-point boundary value problems for linear second order ordinary differential equations was initiated by Il'in and Moiseev [6]. Motivated by [6], Gupta [4] studied certain three-point boundary value problems for nonlinear ordinary differential equations. Since then, more general nonlinear multi-point boundary value problems have been studied by several authors. We refer the reader to [4][5][6][8][9][10] for some relevant references.

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“…This result has been extended and developed by many authors (see Erbe, Hu and Wang [2] and Lian, Wong and Yeh [7] for some references).…”

Section: Then (12) Has At Least One Positive Solution If Eithermentioning

confidence: 63%

Existence of positive solutions for second order m-point boundary value problems

2002

Ann. Polon. Math.

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“…where a(t) = t −1/2 (4/3 − t) −1/2 , f (t,x(t)) = (x(t)) 3 + ln[1 + (x(t)) 2 ], K(t,ζ,x(ζ)) = x(ζ) + ln[1 + (x(ζ)) 3 ]. It can easily be verified that a(t) is nonnegative and pseudo-symmetric about 2/3 on (0,1), f (t,x(t)) and K (t,ζ,x(ζ) 4 = 0. Thus, by Theorem 3.1, there exist extremal positive, concave, and pseudosymmetric solutions for the boundary value problem (3.12).…”

Section: Resultsmentioning

confidence: 99%

“…Investigation of positive solutions of multipoint second-order ordinary boundary value problems, initiated by Il'in and Moiseev [1,2], has been extensively addressed by many authors, for instance, see [3][4][5][6]. Multipoint problems refer to a different family of boundary conditions in the study of disconjugacy theory [7].…”

Section: Introductionmentioning

confidence: 99%

The Monotone Iterative Technique for Three-Point Second-Order Integrodifferential Boundary Value Problems with p-Laplacian

Ahmad

Nieto

2007

Boundary Value Problems

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“…1 Let In order to discuss our main result, we need the follo wing useful lemmas which due to Lian et al 15 and Guo and Lakshmikantham 10 , respectively.…”

Section: Boundary Value Problemsmentioning

confidence: 99%

Existence of Positive Solutions for Nonlinear Eigenvalue Problems

Wang

Wong²,

Kung³

2010

Bound Value Probl

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Existence of solutions for nonlinear BVPs of second-order differential equations on measure chains

Cited by 10 publications

References 10 publications

Existence of positive solutions for second order m-point boundary value problems

Existence of positive solutions for second order m-point boundary value problems

The Monotone Iterative Technique for Three-Point Second-Order Integrodifferential Boundary Value Problems with p-Laplacian

Existence of Positive Solutions for Nonlinear Eigenvalue Problems

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