Open AccessThe Existence and Uniqueness of Positive Solutions of an Ordinary Differential Equation with a Nonlocal Conditions
Author(s) -
E. O. Bin-Taher
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1900/1/012010
Subject(s) - uniqueness , ordinary differential equation , mathematics , order (exchange) , differential equation , function (biology) , mathematical analysis , constant (computer programming) , exact differential equation , computer science , finance , evolutionary biology , economics , biology , programming language
Many researchers have studied problems with non-local conditions of the second-order differential equations. In this work we study the ordinary differential equation v″(t) + g(t, v(t)) = 0, t ∈ (0,1), with the nonlocal conditions v’(1) = 0, v(0) = D α v(t)| t=1 ,α ∈ (0,1). First, we study the existence of at least one positive continuous solution under some assumptions on the function g. Then we discuss the uniqueness of solution by assume that there exist a constant k > 0 such that |g(t,v)-g(t,ῡ)| ≤ |v-ῡ|, ∀ t ∈ [0,1], ∀v, ῡ C[0,1] for this ordinary differential equation, a clarifying example was given as an application. The main idea in this paper is to study ordinary differential equations with a fractional order condition.