Osgood type conditions for an m th-order differential equation

Stanisaw Szufla

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1998)

  • Volume: 18, Issue: 1-2, page 45-55
  • ISSN: 1509-9407

Abstract

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We present a new theorem on the differential inequality u ( m ) ≤ w ( u ) . Next, we apply this result to obtain existence theorems for the equation x ( m ) = f ( t , x ) .

How to cite

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Stanisaw Szufla. "Osgood type conditions for an m th-order differential equation." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 18.1-2 (1998): 45-55. <http://eudml.org/doc/276004>.

@article{StanisawSzufla1998,
abstract = {We present a new theorem on the differential inequality $u^\{(m)\} ≤ w(u)$. Next, we apply this result to obtain existence theorems for the equation $x^\{(m)\} = f(t,x)$.},
author = {Stanisaw Szufla},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {initial value problems; measures of noncompactness; ordinary differential equations; existence of solutions; measure of noncompactness; Osgood type-condition},
language = {eng},
number = {1-2},
pages = {45-55},
title = {Osgood type conditions for an m th-order differential equation},
url = {http://eudml.org/doc/276004},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Stanisaw Szufla
TI - Osgood type conditions for an m th-order differential equation
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1998
VL - 18
IS - 1-2
SP - 45
EP - 55
AB - We present a new theorem on the differential inequality $u^{(m)} ≤ w(u)$. Next, we apply this result to obtain existence theorems for the equation $x^{(m)} = f(t,x)$.
LA - eng
KW - initial value problems; measures of noncompactness; ordinary differential equations; existence of solutions; measure of noncompactness; Osgood type-condition
UR - http://eudml.org/doc/276004
ER -

References

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  1. [1] V. A. Aleksandrov and N. S. Dairbekov, Remarks on the theorem of M. and S. Radulescu about an initial value problem for the differential equation x ( n ) = f ( t , x ) , Rev. Roum. Math. Pure Appl. 37 (1992), 95-102. Zbl0757.34049
  2. [2] A. Cellina, On the existence of solutions of ordinary differential equations in Banach spaces, Funkcial. Ekvac. 14 (1972), 129-136. Zbl0271.34071
  3. [3] P. Hartman, Ordinary Differential Equations, New York - London - Sydney 1964. Zbl0125.32102
  4. [4] J. Januszewski and S. Szufla, On the Urysohn integral equation in locally convex spaces, Publ. Inst. Math. 51 (1992), 77-80. Zbl0776.45010
  5. [5] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), 985-999. Zbl0462.34041
  6. [6] B. N. Sadowskii, Limit - compact and condensing mappings, Russian Math. Surveys 27 (1972), 85-155. 
  7. [7] S. Szufla, On the structure of solutions sets of differential and integral equations in Banach spaces, Ann. Polon. Math. 34 (1977), 165-177. Zbl0384.34038
  8. [8] S. Szufla, On the equation x' = f(t,x) in locally convex spaces, Math. Nachr. 118 (1984), 179-185. Zbl0569.34052
  9. [9] S. Szufla, On the differential equation x ( m ) = f ( t , x ) in Banach spaces, Funkcial. Ekvac. 41 (1998), 101-105. Zbl1140.34400

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