Osgood type conditions for an m th-order differential equation

• Autorzy: Stanisaw Szufla
• Języki publikacji: EN

Abstrakty

EN

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 $x^{(m)} = f(t,x)$.

Słowa kluczowe

EN

initial value problems; measures of noncompactness

Kategorie tematyczne

• 34G20: Nonlinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1998
• Tom: 18
• Numer: 1-2
• Strony: 45-55

Daty

wydano

1998

otrzymano

1998-10-20

Twórcy

autor

Stanisaw Szufla

• Adam Mickiewicz University, Poznań, Poland

Bibliografia

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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.
• [3] P. Hartman, Ordinary Differential Equations, New York - London - Sydney 1964.
• [4] J. Januszewski and S. Szufla, On the Urysohn integral equation in locally convex spaces, Publ. Inst. Math. 51 (1992), 77-80.
• [5] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), 985-999.
• [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.
• [8] S. Szufla, On the equation x' = f(t,x) in locally convex spaces, Math. Nachr. 118 (1984), 179-185.
• [9] S. Szufla, On the differential equation $x^{(m)} = f(t,x)$ in Banach spaces, Funkcial. Ekvac. 41 (1998), 101-105.