Non-linear Semigroup of a Class of Abstract Semilinear Functional Differential Equations with a Non-Dense Domain
Non-linear Semigroup of a Class of Abstract Semilinear Functional Differential Equations with a Non-Dense Domain
摘要
In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett approach,the solutions as a semigroup of non-linear operators.
In this work,we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space.Our objective is to study,using the Crandall-Liggett approach,the solutions as a semigroup of non-linear operators.
参考文献17
-
1Travis, C. C., Webb, G. F.: Existence and stability for partial functional differential equations. Trans.Amer. Math. Soc, 200,395-418 (1974).
-
2Adimy, M., Ezzinbi, K.: Local existence and linearized stability for partial functional differential equations.Dynamic Systems and Applications, 7, 389-404 (1998).
-
3Prato Da, G., Sinestrari, E.: Differential operators with non-dense domains. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 14, 285-344 (1987).
-
4Thieme, H. R.: Semiflows generated by Lipschitz perturbations of non-densely defined operators. Diff. Int.Equat., 3, 1035-1066 (1990).
-
5Yosida, K.: Functional Analysis, 2nd ed., Springer-Verlag, New York 1968.
-
6Crandall, M. G., Liggett, T. M.: Generation of semigroups of nonlinear transformations on general Banach spaces. Amer. J. Math., 93,265-298 (1971).
-
7Adimy, M., Ezzinbi, K.: Spectral Decomposition for Some Partial Functional Differential Equations of Retarded Type, preprint, URS 2055 C.N.R.S Pau 99/28, 1999.
-
8Crandall, M. G.: Differential equations on convex sets. J. Math. Soc. Japan, 22, 443, 455 (1970).
-
9Crandall, M. G., Liggett, T. M.: A theorem and a counter example in the theory of semigroups of nonlinear transformations. Trans. Math. Amer. Soc., 160, 263-278 (1971).
-
10Crandall, M. G.,Pazy, A.: Semigroups of nonlinear contractions and dissipative sets. J. Func. Anal., 3,376-418 (1969).
-
1刘俊先.映射空间中几个定理的扩展[J].邢台师专学报,1994(2):20-22.
-
2孟庆义,胡宗英.非线性半群的生成元与微分方程的解[J].武汉水利电力大学(宜昌)学报,1997,19(4):114-116.
-
3马绍芹.Banach空间中的非线性半群(Ⅳ)[J].天津商学院学报,1989,9(2):37-50.
-
4马绍芹.Banach空间中的非线性半群(Ⅴ)[J].天津商学院学报,1989,9(3):25-34.
-
5张康培.一类非线性泛函数分方程解的有界性[J].安徽大学学报(自然科学版),1991,15(1):1-4.
-
6张石生,康世焜,丁佐华.含非线性半群的微分包含[J].成都科技大学学报,1992(2):29-33.
-
7张康培.关于抽象泛函微分方程与乘积空间上的非线性半群[J].数学年刊(A辑),1989,10(1):40-50. 被引量:2
-
8孙斌.解析函数收敛性的拓扑方法[J].广东科技,2013,22(22):207-208.
-
9沈冲,姚卫.函数式积拓扑:和拓扑、积拓扑和点式收敛拓扑的共同推广[J].河北科技大学学报,2015,36(4):390-393.