# Existence of positive solutions for a class of second-order two-point boundary value problem

Existence of positive solutions for a class of second-order two-point boundary value problem By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order two-point boundary value problem $$\left\{\begin{array}{l} \varphi^{\prime\prime}(t) + h(t)f(\varphi(t)) = 0,\,\, 0 < t < 1,\\ \alpha\varphi(0) - \beta\varphi^{\prime}(0) = 0,\,\, \gamma\varphi(1) + \delta\varphi^{\prime}(1) = 0, \end{array}\right.$$ is obtained under some conditions of growth, where α, β, γ, δ ≥ 0, ρ = αγ + γβ + δα > 0, and h(t) is allowed to be singular at t = 0 and t = 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Existence of positive solutions for a class of second-order two-point boundary value problem

, Volume 12 (3) – Mar 12, 2008
8 pages

/lp/springer_journal/existence-of-positive-solutions-for-a-class-of-second-order-two-point-Kk2JvndBGg
Publisher
Springer Journals
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2159-6
Publisher site
See Article on Publisher Site

### Abstract

By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order two-point boundary value problem $$\left\{\begin{array}{l} \varphi^{\prime\prime}(t) + h(t)f(\varphi(t)) = 0,\,\, 0 < t < 1,\\ \alpha\varphi(0) - \beta\varphi^{\prime}(0) = 0,\,\, \gamma\varphi(1) + \delta\varphi^{\prime}(1) = 0, \end{array}\right.$$ is obtained under some conditions of growth, where α, β, γ, δ ≥ 0, ρ = αγ + γβ + δα > 0, and h(t) is allowed to be singular at t = 0 and t = 1.

### Journal

PositivitySpringer Journals

Published: Mar 12, 2008

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