In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.
@article{119184, author = {Mouffak Benchohra and Sotiris K. Ntouyas}, title = {Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {41}, year = {2000}, pages = {485-491}, zbl = {1045.34036}, mrnumber = {1795080}, language = {en}, url = {http://dml.mathdoc.fr/item/119184} }
Benchohra, Mouffak; Ntouyas, Sotiris K. Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 485-491. http://gdmltest.u-ga.fr/item/119184/
Existence and uniqueness of mild solutions of a semilinear evolution equation with nonlocal conditions, Indian J. Pure Appl. Math. 25 (1994), 411-418. (1994) | MR 1272813
Existence of solutions of nonlinear integrodifferential equation with nonlocal conditions, J. Appl. Math. Stoch. Anal. 10 (1996), 279-288. (1996) | MR 1468123
Nonlocal Cauchy problem for quasilinear integrodifferential equation in Banach spaces, Dynam. Systems Appl. 8 (1999), 35-44. (1999) | MR 1669065 | Zbl 0924.34056
Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (1996), 443-449. (1996) | MR 1387239 | Zbl 0854.34065
Existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problem, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. 18 (1993), 109-112. (1993) | MR 1274697
Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505. (1991) | MR 1137634 | Zbl 0748.34040
Integral Equations and Applications, Cambridge Univ. Press New York (1990). (1990) | MR 1109491
Existence of solutions for an integrodifferential equation with nonlocal condition in Banach spaces, Libertas Math. 16 (1996), 133-143. (1996) | MR 1412536 | Zbl 0862.45016
Fixed Point Theory, Monografie Mat., PWN, Warsaw, 1982. | MR 0660439 | Zbl 1025.47002
Semigroups of Linear Operators and Applications, Oxford New York (1985). (1985) | MR 0790497 | Zbl 0592.47034
Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679-687. (1997) | MR 1453198 | Zbl 0884.34069
Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions, Appl. Anal. 64 (1997), 99-105. (1997) | MR 1460074 | Zbl 0874.35126
Functional Analysis, Springer-Verlag Berlin (1980). (1980) | MR 0617913 | Zbl 0435.46002