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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 363089, 5 pages
http://dx.doi.org/10.1155/2014/363089
Research Article

A Parameter Property of Classical Solutions of Cauchy Problems

Kent State University at Trumbull, Warren, OH 44483, USA

Received 1 November 2013; Accepted 26 December 2013; Published 10 February 2014

Academic Editor: Yuming Xing

Copyright © 2014 Min He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. W. Brewer, “A parameter dependence problem in functional-differential equations,” in Volterra and Functional-Differential Equations, vol. 81 of Lecture Notes in Pure and Applied Mathematics, pp. 187–195, Dekker, New York, NY, USA, 1982. View at Zentralblatt MATH · View at MathSciNet
  2. R. Grimmer and M. He, “Fixed point theory and nonlinear periodic systems,” The CUBO Mathematical Journal, vol. 11, no. 3, pp. 101–104, 2009. View at Zentralblatt MATH · View at MathSciNet
  3. M. He, “A class of integrodifferential equations with memory,” Semigroup Forum, vol. 73, no. 3, pp. 427–443, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. He, “On continuity in parameters of integrated semigroups,” Discrete and Continuous Dynamical Systems A, pp. 403–412, 2003. View at Zentralblatt MATH · View at MathSciNet
  5. C. Lizama, “On the convergence and approximation of integrated semigroups,” Journal of Mathematical Analysis and Applications, vol. 181, no. 1, pp. 89–103, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Nicaise, “The Hille-Yosida and Trotter-Kato theorems for integrated semigroups,” Journal of Mathematical Analysis and Applications, vol. 180, no. 2, pp. 303–316, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Busenberg and B. Wu, “Convergence theorems for integrated semigroups,” Differential and Integral Equations, vol. 5, no. 3, pp. 509–520, 1992. View at Zentralblatt MATH · View at MathSciNet
  8. H. R. Thieme, “‘Integrated semigroups’ and integrated solutions to abstract Cauchy problems,” Journal of Mathematical Analysis and Applications, vol. 152, no. 2, pp. 416–447, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Arendt, “Vector-valued Laplace transforms and Cauchy problems,” Israel Journal of Mathematics, vol. 59, no. 3, pp. 327–352, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Da Prato and E. Sinestrari, “Differential operators with nondense domain,” Annali della Scuola Normale Superiore di Pisa, vol. 14, no. 2, pp. 285–344, 1987. View at MathSciNet
  11. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44, Springer, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at MathSciNet