Positive solutions for the boundary value problem (|u″|p−2u″)″− λq(t)f(u(t)) = 0

Ravi P. Agarwal; Haishen Lü; Donal O’Regan

Positive solutions for the boundary value problem (|u″|^p−2u″)″− λq(t)f(u(t)) = 0

Ravi P. Agarwal
, Haishen Lü
, Donal O’Regan

Mathematics

Department of Mathematical Sciences
Second Hospital of Lanzhou University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

9 Citations (Scopus)

Abstract

This paper considers the boundary value problem: (Formula Presented), with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. Moreover, we derive an explicit interval for λ such that for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition we also discuss the existence of two positive solutions for λ in an appropriate interval.

Original language	English
Pages (from-to)	33-44
Number of pages	12
Journal	Memoirs on Differential Equations and Mathematical Physics
Volume	28
Publication status	Published - 2003

Keywords

Beam equation
Boundary value problem
Positive solution

Cite this

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abstract = "This paper considers the boundary value problem: (Formula Presented), with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. Moreover, we derive an explicit interval for λ such that for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition we also discuss the existence of two positive solutions for λ in an appropriate interval.",

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journal = "Memoirs on Differential Equations and Mathematical Physics",

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AU - Agarwal, Ravi P.

AU - Lü, Haishen

AU - O’Regan, Donal

PY - 2003

Y1 - 2003

N2 - This paper considers the boundary value problem: (Formula Presented), with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. Moreover, we derive an explicit interval for λ such that for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition we also discuss the existence of two positive solutions for λ in an appropriate interval.

AB - This paper considers the boundary value problem: (Formula Presented), with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. Moreover, we derive an explicit interval for λ such that for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition we also discuss the existence of two positive solutions for λ in an appropriate interval.

KW - Beam equation

KW - Boundary value problem

KW - Positive solution

UR - https://www.scopus.com/pages/publications/27644590231

M3 - Article

AN - SCOPUS:27644590231

SN - 1512-0015

VL - 28

SP - 33

EP - 44

JO - Memoirs on Differential Equations and Mathematical Physics

JF - Memoirs on Differential Equations and Mathematical Physics

ER -

Positive solutions for the boundary value problem (|u″|^p−2u″)″− λq(t)f(u(t)) = 0

Abstract

Keywords

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