An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities

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

doi:10.7153/mia-11-05

An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities

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

Mathematics

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

6 Citations (Scopus)

Abstract

This paper presents new existence results for the singular boundary value problem { -u = g (t,u) + λh (t,u), t ∈ (0,1) u(0) = 0 = u (1). In particular our nonlinearity may be singular at t = 0,1 and u = 0 and is allowed to change sign. Existence in this paper will be established by obtaining a sequence of upper and lower solutions which in turn will generate a sequence of approximate solutions.

Original language	English
Pages (from-to)	81-98
Number of pages	18
Journal	Mathematical Inequalities and Applications
Volume	11
Issue number	1
DOIs	https://doi.org/10.7153/mia-11-05
Publication status	Published - Jan 2008

Keywords

Positive solution
Singular boundary value problems
Upper and lower solution

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abstract = "This paper presents new existence results for the singular boundary value problem \{ -u = g (t,u) + λh (t,u), t ∈ (0,1) u(0) = 0 = u (1). In particular our nonlinearity may be singular at t = 0,1 and u = 0 and is allowed to change sign. Existence in this paper will be established by obtaining a sequence of upper and lower solutions which in turn will generate a sequence of approximate solutions.",

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AU - O'Regan, Donal

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N2 - This paper presents new existence results for the singular boundary value problem { -u = g (t,u) + λh (t,u), t ∈ (0,1) u(0) = 0 = u (1). In particular our nonlinearity may be singular at t = 0,1 and u = 0 and is allowed to change sign. Existence in this paper will be established by obtaining a sequence of upper and lower solutions which in turn will generate a sequence of approximate solutions.

AB - This paper presents new existence results for the singular boundary value problem { -u = g (t,u) + λh (t,u), t ∈ (0,1) u(0) = 0 = u (1). In particular our nonlinearity may be singular at t = 0,1 and u = 0 and is allowed to change sign. Existence in this paper will be established by obtaining a sequence of upper and lower solutions which in turn will generate a sequence of approximate solutions.

KW - Positive solution

KW - Singular boundary value problems

KW - Upper and lower solution

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DO - 10.7153/mia-11-05

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EP - 98

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities

Abstract

Keywords

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