We present a new theorem on the differential inequality . Next, we apply this result to obtain existence theorems for the equation .
@article{bwmeta1.element.bwnjournal-article-div18i1-2n4bwm, author = {Stanisaw Szufla}, title = {Osgood type conditions for an m th-order differential equation}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {18}, year = {1998}, pages = {45-55}, zbl = {0932.34062}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div18i1-2n4bwm} }
Stanisaw Szufla. Osgood type conditions for an m th-order differential equation. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 18 (1998) pp. 45-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div18i1-2n4bwm/
[000] [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 , Rev. Roum. Math. Pure Appl. 37 (1992), 95-102. | Zbl 0757.34049
[001] [2] A. Cellina, On the existence of solutions of ordinary differential equations in Banach spaces, Funkcial. Ekvac. 14 (1972), 129-136. | Zbl 0271.34071
[002] [3] P. Hartman, Ordinary Differential Equations, New York - London - Sydney 1964. | Zbl 0125.32102
[003] [4] J. Januszewski and S. Szufla, On the Urysohn integral equation in locally convex spaces, Publ. Inst. Math. 51 (1992), 77-80. | Zbl 0776.45010
[004] [5] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), 985-999. | Zbl 0462.34041
[005] [6] B. N. Sadowskii, Limit - compact and condensing mappings, Russian Math. Surveys 27 (1972), 85-155.
[006] [7] S. Szufla, On the structure of solutions sets of differential and integral equations in Banach spaces, Ann. Polon. Math. 34 (1977), 165-177. | Zbl 0384.34038
[007] [8] S. Szufla, On the equation x' = f(t,x) in locally convex spaces, Math. Nachr. 118 (1984), 179-185. | Zbl 0569.34052
[008] [9] S. Szufla, On the differential equation in Banach spaces, Funkcial. Ekvac. 41 (1998), 101-105. | Zbl 1140.34400