nagumo condition
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Successive approximations for a differential equation in a Banach space via Constantin condition

2021 ◽  
Vol 71 (1) ◽  
pp. 105-116
Author(s):  
Aldona Dutkiewicz ◽  
Mirosława Zima
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Cauchy Problem ◽  
Unique Solution ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Successive Approximations ◽  
First Order ◽  
Nagumo Condition ◽  
Kuratowski Measure Of Noncompactness

Abstract We give some sufficient conditions for the convergence of the sequence of successive approximations to the unique solution of first order Cauchy problem in a Banach space. Our approach is based on a generalized Nagumo condition due to A. Constantin and the properties of the Kuratowski measure of noncompactness.

Existence result for a class of nonlinear third-order two-point boundary-value problems

2009 ◽  
Vol 52 (3) ◽  
pp. 787-796
Author(s):  
Libo Wang ◽  
Minghe Pei ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problems ◽  
Existence Result ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Degree Theory ◽  
Point Boundary ◽  
Third Order ◽  
Nagumo Condition ◽  
Sign Type

AbstractThe upper and lower solutions method and Leray–Schauder degree theory are employed to establish the existence result for a class of nonlinear third-order two-point boundary-value problems with a sign-type Nagumo condition.

Higher order nonlinear two-point boundary value problems with sign-type Nagumo condition

2009 ◽  
Author(s):  
Maria do Rosário Grossinho ◽  
Feliz Minhós ◽  
Ana Isabel Santos ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
Nagumo Condition ◽  
Sign Type

A third-order boundary value problem with one-sided Nagumo condition

2005 ◽  
Vol 63 (5-7) ◽  
pp. e247-e256 ◽  
Author(s):  
M.R. Grossinho ◽  
F.M. Minhós ◽  
A.I. Santos
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Third Order ◽  
Nagumo Condition

Examples of the nonexistence of a solution in the presence of upper and lower solutions

2003 ◽  
Vol 44 (4) ◽  
pp. 591-594 ◽  
Author(s):  
Patrick Habets ◽  
Rodrigo L. Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Second Order ◽  
Lower And Upper Solutions ◽  
Existence Of A Solution ◽  
Nagumo Condition

AbstractStandard results for boundary value problems involving second-order ordinary differential equations ensure that the existence of a well-ordered pair of lower and upper solutions together with a Nagumo condition imply existence of a solution. In this note we introduce some examples which show that existence is not guaranteed if no Nagumo condition is satisfied.

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