Existence of solutions for neutral functional differential evolution equations with nonlocal conditions. (English) Zbl 1034.34096

By employing fractional power of operators and Sadovskii’s fixed-point theorem, the authors study the existence of mild and strong solutions to semilinear neutral functional-differential evolution equations with nonlocal conditions.


34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
Full Text: DOI


[1] Balachandran, K.; Chandrasekaran, M., Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math., 27, 443-449 (1996) · Zbl 0854.34065
[2] Byszewski, L., Theorems about the existence and uniqueness of a solution of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162, 496-505 (1991) · Zbl 0748.34040
[3] Byszewski, L., Existence, uniqueness and asymptotic stability of solutions of abstract non-local Cauchy problems, Dynamics Systems Appl., 5, 595-606 (1996) · Zbl 0869.47034
[4] Byszewski, L., On weak solutions of functional differential abstract nonlocal Cauchy problem, Ann. Polon. Math., 65, 163-170 (1997) · Zbl 0874.47026
[5] Byszewski, L., Application of properties of the right-hand sides of evolution equation to an investigation of nonlocal evolution problem, Nonlinear Anal., 33, 413-426 (1998) · Zbl 0933.34064
[6] Byszewski, L.; Akca, H., Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Anal., 34, 65-72 (1998) · Zbl 0934.34068
[7] Byszewski, L.; Lakshimikantham, V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40, 11-19 (1990) · Zbl 0694.34001
[8] Hernandez, E.; Henriquez, H. R., Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl., 221, 452-475 (1998) · Zbl 0915.35110
[9] Lin, Y.; Liu, H., Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal., 26, 1023-1033 (1996) · Zbl 0916.45014
[10] Marle, C. M., Mesures et Probabilities (1974), Hermam: Hermam Paris · Zbl 0306.28001
[11] Ntouyas, S. K.; Tsamatos, P. Ch., Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl., 210, 679-687 (1997) · Zbl 0884.34069
[12] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer: Springer New York · Zbl 0516.47023
[13] Sadovskii, B. N., On a fixed point principle, Funct. Anal. Appl., 1, 74-76 (1967) · Zbl 0165.49102
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