Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem

Yan Sun; Yeol Je Cho; Donal O'Regan

doi:10.1016/j.amc.2008.11.025

Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem

Yan Sun
, Yeol Je Cho
, Donal O'Regan

Mathematics

Shanghai Normal University
Natural Sciences College of Education

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

26 Citations (Scopus)

Abstract

In this paper, we consider the existence of positive solutions for the singular second order Neumann boundary value problem. fenced((x^″ + k² x = f (t) g (t, x), 0 < t < 1,; x^′ (0) = x^′ (1) = 0 ;))where k ∈ (0, frac(π, 2)) is a constant, g (t, x) is monotone locally with respect to x and f (t), g (t, x) may be singular at t = 0, t = 1 and x = 0.

Original language	English
Pages (from-to)	80-86
Number of pages	7
Journal	Applied Mathematics and Computation
Volume	210
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2008.11.025
Publication status	Published - 1 Apr 2009

Keywords

Fixed point theory
Positive solution
Singular Neumann boundary value problem

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Sun, Y;Cho, YJ;O'Regan, D

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10.1016/j.amc.2008.11.025

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abstract = "In this paper, we consider the existence of positive solutions for the singular second order Neumann boundary value problem. fenced((x″ + k2 x = f (t) g (t, x), 0 < t < 1,; x′ (0) = x′ (1) = 0 ;))where k ∈ (0, frac(π, 2)) is a constant, g (t, x) is monotone locally with respect to x and f (t), g (t, x) may be singular at t = 0, t = 1 and x = 0.",

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N2 - In this paper, we consider the existence of positive solutions for the singular second order Neumann boundary value problem. fenced((x″ + k2 x = f (t) g (t, x), 0 < t < 1,; x′ (0) = x′ (1) = 0 ;))where k ∈ (0, frac(π, 2)) is a constant, g (t, x) is monotone locally with respect to x and f (t), g (t, x) may be singular at t = 0, t = 1 and x = 0.

AB - In this paper, we consider the existence of positive solutions for the singular second order Neumann boundary value problem. fenced((x″ + k2 x = f (t) g (t, x), 0 < t < 1,; x′ (0) = x′ (1) = 0 ;))where k ∈ (0, frac(π, 2)) is a constant, g (t, x) is monotone locally with respect to x and f (t), g (t, x) may be singular at t = 0, t = 1 and x = 0.

KW - Fixed point theory

KW - Positive solution

KW - Singular Neumann boundary value problem

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ER -

Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem

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Keywords

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