Abstract
We consider the following second order differential equation with delay (Equation) In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality (Equation) is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case 0<γi≤1,0<δi≤1 for i = 1,..., p.
Original language | English |
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Pages (from-to) | 339-362 |
Number of pages | 24 |
Journal | Opuscula Mathematica |
Volume | 34 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2014 |
Externally published | Yes |
Keywords
- Boundary value problem
- Green's functions
- Impulsive equations
- Positivity/negativity of green's functions
- Second order
ASJC Scopus subject areas
- General Mathematics