Solubility of the Cauchy problem for differential equations in scales of Banach spaces with completely continuous embeddings

1994 ◽  
Vol 55 (4) ◽  
pp. 372-379
Author(s):  
V. I. Nazarov
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Completely Continuous ◽  
The Cauchy Problem ◽  
Scales Of Banach Spaces

On the Cauchy problem for ordinary differential equations in Banach spaces

1982 ◽  
Vol 39 (2) ◽  
pp. 153-160 ◽  
Author(s):  
Harald Mönch ◽  
Gerd-Friedrich von Harten
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
The Cauchy Problem

scholarly journals On existence theorems for differential equations in Banach spaces

1985 ◽  
Vol 32 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Józef Banaś
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
Existence Theorems ◽  
The Cauchy Problem

In this paper we show that a number of existence theorems for the Cauchy problem of ordinary differential equations in Banach spaces are only apparent generalizations of the previous ones.

scholarly journals Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Ezzat R. Hassan ◽  
M. Sh. Alhuthali ◽  
M. M. Al-Ghanmi
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Uniqueness Theorem ◽  
Banach Spaces ◽  
Nonlinear Ordinary Differential Equations ◽  
Empty Interior ◽  
Reflexive Banach Spaces ◽  
Uniqueness Criterion ◽  
The Cauchy Problem

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

scholarly journals Kneser's theorem for differential equations in Banach spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 419-434 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Vector Field ◽  
Differential Equations ◽  
Banach Spaces ◽  
Measure Of Noncompactness ◽  
Solution Set ◽  
The Cauchy Problem ◽  
Uniformly Continuous

We consider the Cauchy problem x (t) = f (t,x (t)), x (O) = xO defined in a nonreflexive Banach space and with the vector field f: T × X → X being weakly uniformly continuous. Using a compactness hypothesis that involves the weak measure of noncompactness, we prove that the solution set of the above Cauchy problem is nonempty, connected and compact in .

scholarly journals On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Malkhaz Ashordia ◽  
Inga Gabisonia ◽  
Mzia Talakhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
The Cauchy Problem ◽  
Generalized Ordinary Differential Equations

AbstractEffective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals An Application Of The Theory Of Scale Of Banach Spaces

2015 ◽  
Vol 29 (1) ◽  
pp. 51-59
Author(s):  
Łukasz Dawidowski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Banach Spaces ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Selection Of

AbstractThe abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

Sign in / Sign up

Export Citation Format

Share Document