Existence of mild solutions for abstract mixed type semilinear evolution equations

Turkish Journal of Mathematics

Volumn 35, Issue 3, 2011, Pages 457-472

  Shi, Hong Bo ^a,b   Li, Wan Tong ^a   Sun, Hong Rui ^a  

^a LANZHOU UNIVERSITY   (China)

^b HUAIYIN NORMAL UNIVERSITY   (China)

Author keywords

C0 semigroup; Convex power condensing operator; Fixed point theorem; Measure of noncompactness; Semilinear evolution equation

Indexed keywords

EID: 80054905923     PISSN: 13000098     EISSN: 13036149     Source Type: Journal    
DOI: 10.3906/mat-0905-29     Document Type: Article

References (21)

1. Chang Y.K.: Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos, Solitons & Fractals, 33, 1601-1609 (2007).
2. Chang Y.K. and Nieto J.: Some new existence results for fractional differential inclusions with boundary conditions, Math. Computer Modelling, 49, 605-609 (2009).
3. Deimling K.: Nonlinear Functional Analysis, Springer-Verlag, New York, 1985.
4. Guo D. and Lakshmikantham V.: Nonlinear Problems in Abstract Cones, Academic press, San Diego, 1988.
5. Guo D., Lakshmikantham V. and Liu X.: Nonlinear Integral Equations in Abstract Cones, Kluwer Academic Publishers, Dordrecht, 1996.
6. Li Y.: The positive solutions of abstract semilinear evolution equations and their applications (in Chinese), Acta Math. Sinica, 39, 666-672 (1996).
7. Li Y.: Periodic solutions of abstract semilinear evolution equations in Banach spaces (in Chinese), Acta Math. Sinica, 41, 629-636 (1998).
8. Li Y.: Existence of solutions of initial value problems for abstract semilinear evolution equations (in Chinese), Acta Math. Sinica, 48, 1089-1094 (2005).
9. Li Y.: Existence and uniqueness of periodic solution for a class of semilinear evolution equations, J. Math. Anal. Appl., 349, 226-234 (2009).
10. Liang J., Liu J. and Xiao T.: Nonlocal Cauchy problems governed by compact operator families, Nonlinear Anal., 57, 183-189 (2004).
11. Liang J., Liu J. and Xiao T.: Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Modelling, 49, 798-804 (2009).
12. Liang J., Liu J. and Xiao T.: Semilinear integrodifferential equations with nonlocal initial conditions, Comput. Math. Appl., 47, 863-875 (2004).
13. Lin Y. and Liu J.: Semilinear integrodifferential equations with local Cauchy problem, Nonlinear Anal., 26, 1023-1033 (1996).
14. Liu L.: Existence of global solutions of initial value problem for nonlinear integro-differential equations of mixed type in Banach spaces (in Chinese), J. System Sci. Math., 20, 112-116 (2000).
15. Liu L., Guo F., Wu C. and Wu Y.: Existence theorems of global solutions of nonlinear Volterra type integral equations in Banach spaces, J. Math. Anal. Appl., 309, 638-649 (2005).
16. Pazy A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
17. Sadovskii B.: A fixed point principle, Functional Anal. Appl., 1, 151-153 (1967).
18. Sun J. and Zhang X.: The fixed point theorem of convex-power condensing operator and applications to abstract semilinear evolution equations (in Chinese), Acta Math. Sinica, 48, 439-446 (2005).
19. Vasile I.: Fixed Point Theorem, D. Reidel Publishing Press, Dordrecht, 1981.
20. Zhang X.: Fixed point theorems for a class of nonlinear operator in Banach spaces and applications, Nonlinear Anal., 69, 536-543 (2008).
21. Zhang G., Zhang T. and Zhang T.: Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application, Appl. Math. Comput., 214, 618-623 (2009).