Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
Existence of Triple Positive Solutions for Nonlinear Second Order Arbitrary Two-point Boundary Value Problems
Asaduzzaman, M. and Ali, M. Z.
Corresponding Email: asad@math.iu.ac.bd
Received date: 30 December 2019
Accepted date: 1 August 2020
Abstract:
In this paper, we establish the criteria for existence of triple positive solutions to the nonlinear second order ordinary differential equation
\(u^{''}(t)+f(t, u(t), u^{'}(t))=0\), \(t \in [a, b]\), with the arbitrary two-point boundary value conditions \(u(a)=u(b)=0\), where, \(a\), \(b\) are two arbitrary non-negative constants and \(f \in C ([a, b] \times [0, \inf) \times \mathbb{R}, [0, \inf))\). The analysis of this paper is based on a fixed point theorem of functional type in a cone due to Bai and Ge. The result of this paper generalizes the results of several authors in literature. Finally, we give an illustrative example to support our analytic proof.
Keywords: Nonlinear second order arbitrary two-point boundary value problem, Triple positive solutions, Fixed point theorem
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