The infinite generator of α-times
Integrated C semigroups and the
properties of resolvent are given. At the same time, we discuss the
relationship between the existence of strong solution of a class of
nonhomogeneous abstract Cauchy problem andα-times integrated C semigroups, and a sufficient and necessary condition is
obtained.
References
[1]
F. M. Neubrander, “Integrated Semigroups and Their Applications to the Abstract Cauchy Problem,” Pacific Journal of Mathematics, Vol. 35, No. 1, 1988, pp. 111-155.
doi:10.2140/pjm.1988.135.111
[2]
H. R. Thieme, “‘Integrated Semigroup’ and Integrated Solution to Abstract Cauchy Problem,” Journal of Mathematical Analysis and Applications, Vol. 152, No. 2, 1990, pp. 416-447. doi:10.1016/0022-247X(90)90074-P
[3]
H. Kelleman and M. Heber, “Integrated Semigroups,” Journal of Functional Analysis, Vol. 84, No. 1, 1989, pp. 160-180. doi:10.1016/0022-1236(89)90116-X
[4]
N. U. Ahmed, “Semigroup Theory with Application to System and Control,” Longman Scientific and Technical Press, New York, 1991, p. 58.
[5]
N. U. Ahmed, “Generalized Solution for Linear System Governed by Operators beyond Hille-Yosida Type,” Publication Mathematical Debrecen, Vol. 48, No. 1, 1996, pp. 45-64.
