Previous |  Up |  Next

Article

Keywords:
nonlinear functional differential equations
Summary:
It is proved that nonincreasing and satisfying the Volterra condition right-hand side of a functional differential equation does not guarantee the uniqueness of solutions.
References:
[1] F. E. Browder: Non-linear equations of evolution. Ann. Math. 80 (1964), 485-523. DOI 10.2307/1970660 | MR 0173960 | Zbl 0127.33602
[2] J. B. Diaz R. J. Weinacht: On nonlinear differential equations in Hilbert spaces. Appl. Anal. 1 (1971), 31-41. DOI 10.1080/00036817108839004 | MR 0282032
[3] J. K. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York, 1977. MR 0508721 | Zbl 0352.34001
[4] S. Kato: On existence and uniqueness conditions for nonlinear ordinary differential equation in Banach space. Funkcial. Ekvac. 19 (1976), 239-245. MR 0435538
[5] L. A. Medeiros: On nonlinear differential equations in Hilbert spaces. Amer. Math. Monthly 76 (1969), 1024-1027. DOI 10.1080/00029890.1969.12000396 | MR 0248433
Partner of
EuDML logo