On a singular boundary value problem for the differential equation f (t, x, x , x )=0 using barrier strips

Donal O'Regan

doi:10.1016/j.na.2005.10.008

On a singular boundary value problem for the differential equation f (t, x, x , x )=0 using barrier strips

Donal O'Regan

Mathematics

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Abstract

A method to solve a singular boundary value problem for the differential equation f(t, x, x^′, x^″) = 0 using barrier strips, is discussed. The method was devoted to the solvability of various singular BVPs for ordinary differential equations, whose nonlinearity does not depend on the highest derivative. Various nonsingular BVPs for second-order differential equations, whose nonlinearity depended on x^″, were also investigated. The results show that a differential equation with impulse effects was used to satisfy the nonlinear Carathéodory conditions.

Original language	English (Ireland)
Pages (from-to)	1348-1361
Number of pages	14
Journal	Nonlinear Analysis-Theory Methods & Applications
Volume	65
Issue number	7
DOIs	https://doi.org/10.1016/j.na.2005.10.008
Publication status	Published - 1 Oct 2006

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Authors
Kelevedjiev, PS,O'Regan, D,Popivanov, NI

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10.1016/j.na.2005.10.008

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title = "On a singular boundary value problem for the differential equation f (t, x, x , x )=0 using barrier strips",

abstract = "A method to solve a singular boundary value problem for the differential equation f(t, x, x′, x″) = 0 using barrier strips, is discussed. The method was devoted to the solvability of various singular BVPs for ordinary differential equations, whose nonlinearity does not depend on the highest derivative. Various nonsingular BVPs for second-order differential equations, whose nonlinearity depended on x″, were also investigated. The results show that a differential equation with impulse effects was used to satisfy the nonlinear Carath{\'e}odory conditions.",

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AB - A method to solve a singular boundary value problem for the differential equation f(t, x, x′, x″) = 0 using barrier strips, is discussed. The method was devoted to the solvability of various singular BVPs for ordinary differential equations, whose nonlinearity does not depend on the highest derivative. Various nonsingular BVPs for second-order differential equations, whose nonlinearity depended on x″, were also investigated. The results show that a differential equation with impulse effects was used to satisfy the nonlinear Carathéodory conditions.

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JO - Nonlinear Analysis-Theory Methods & Applications

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On a singular boundary value problem for the differential equation f (t, x, x , x )=0 using barrier strips

Abstract

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