# Osgood type conditions for an m th-order differential equation

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

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

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topStanisaw 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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- [2] A. Cellina, On the existence of solutions of ordinary differential equations in Banach spaces, Funkcial. Ekvac. 14 (1972), 129-136. Zbl0271.34071
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- [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] B. N. Sadowskii, Limit - compact and condensing mappings, Russian Math. Surveys 27 (1972), 85-155.
- [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] S. Szufla, On the equation x' = f(t,x) in locally convex spaces, Math. Nachr. 118 (1984), 179-185. Zbl0569.34052
- [9] S. Szufla, On the differential equation ${x}^{\left(m\right)}=f(t,x)$ in Banach spaces, Funkcial. Ekvac. 41 (1998), 101-105. Zbl1140.34400

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