Well-posedness of initial value problems for functional differential and algebraic equations of mixed type

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2011.30.737 ◽

2011 ◽

Vol 30 (3) ◽

pp. 737-765 ◽

Cited By ~ 4

Author(s):

Hermen Jan Hupkes ◽

◽

Emmanuelle Augeraud-Véron ◽

Keyword(s):

Initial Value Problems ◽

Mixed Type ◽

Well Posedness ◽

Algebraic Equations ◽

Initial Value ◽

Equations Of Mixed Type ◽

Functional Differential

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Discontinuous initial value problems for functional differential–algebraic equations of mixed type

Journal of Differential Equations ◽

10.1016/j.jde.2012.06.012 ◽

2012 ◽

Vol 253 (7) ◽

pp. 1959-2024 ◽

Cited By ~ 9

Author(s):

H. dʼAlbis ◽

E. Augeraud-Véron ◽

H.J. Hupkes

Keyword(s):

Initial Value Problems ◽

Mixed Type ◽

Differential Algebraic Equations ◽

Algebraic Equations ◽

Initial Value ◽

Equations Of Mixed Type ◽

Functional Differential

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Global solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.07.103 ◽

2007 ◽

Vol 330 (2) ◽

pp. 1139-1151 ◽

Cited By ~ 2

Author(s):

Hua Su ◽

Lishan Liu ◽

Xiaoyan Zhang ◽

Yonghong Wu

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Initial Value Problems ◽

Mixed Type ◽

Global Solutions ◽

Second Order ◽

Initial Value ◽

Equations Of Mixed Type

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Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces

Nonlinear Analysis ◽

10.1016/j.na.2005.09.004 ◽

2006 ◽

Vol 64 (11) ◽

pp. 2562-2574 ◽

Cited By ~ 10

Author(s):

Xinguang Zhang ◽

Lishan Liu

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Initial Value Problems ◽

Mixed Type ◽

Second Order ◽

Initial Value ◽

Equations Of Mixed Type

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A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/s0022-247x(02)00366-9 ◽

2002 ◽

Vol 275 (1) ◽

pp. 369-385 ◽

Cited By ~ 20

Author(s):

Li Shan Liu ◽

Congxin Wu ◽

Fei Guo

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Unique Solution ◽

Initial Value Problems ◽

Mixed Type ◽

Initial Value ◽

First Order ◽

Equations Of Mixed Type

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Absolutely continuous global solutions of the initial value problem for neutral functional differential equations of mixed type

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/bf02844656 ◽

1981 ◽

Vol 30 (3) ◽

pp. 435-452 ◽

Cited By ~ 1

Author(s):

V. G. Angelov ◽

D. D. Bainov

Keyword(s):

Differential Equations ◽

Initial Value Problem ◽

Mixed Type ◽

Functional Differential Equations ◽

Global Solutions ◽

Initial Value ◽

Neutral Functional Differential Equations ◽

Absolutely Continuous ◽

Equations Of Mixed Type ◽

Functional Differential

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A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations

Journal of Differential Equations ◽

10.1016/j.jde.2017.04.038 ◽

2017 ◽

Vol 263 (6) ◽

pp. 3491-3532 ◽

Cited By ~ 3

Author(s):

Junya Nishiguchi

Keyword(s):

Differential Equations ◽

Initial Value Problems ◽

Functional Differential Equations ◽

Well Posedness ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Initial Value ◽

Retarded Functional Differential Equations ◽

Functional Differential ◽

Necessary And Sufficient

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Global solutions of initial value problems for nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces

Nonlinear Analysis ◽

10.1016/j.na.2005.02.028 ◽

2005 ◽

Vol 61 (8) ◽

pp. 1363-1382 ◽

Cited By ~ 5

Author(s):

Fei Guo ◽

Lishan Liu ◽

Yonghong Wu ◽

Peg-Foo Siew

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Initial Value Problems ◽

Mixed Type ◽

Global Solutions ◽

Second Order ◽

Initial Value ◽

Equations Of Mixed Type

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Existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(04)90002-8 ◽

2004 ◽

Vol 47 (1) ◽

pp. 13-22 ◽

Cited By ~ 16

Author(s):

Lishan Liu ◽

Congxin Wu ◽

Fei Guo

Keyword(s):

Banach Spaces ◽

Initial Value Problems ◽

Mixed Type ◽

Existence Theorems ◽

Global Solutions ◽

Integrodifferential Equations ◽

Initial Value ◽

Equations Of Mixed Type

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The solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces

Nonlinear Analysis ◽

10.1016/j.na.2006.01.002 ◽

2007 ◽

Vol 66 (5) ◽

pp. 1025-1036 ◽

Cited By ~ 3

Author(s):

Hua Su ◽

Lishan Liu ◽

Xiaoyan Zhang

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Initial Value Problems ◽

Mixed Type ◽

Second Order ◽

Initial Value ◽

Equations Of Mixed Type

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Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.32.2001.346 ◽

2001 ◽

Vol 32 (4) ◽

pp. 315-325

Author(s):

M. Benchohra ◽

S. K. Ntouyas

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Banach Spaces ◽

Initial Value Problems ◽

Existence Of Solutions ◽

Existence Results ◽

Second Order ◽

Initial Value ◽

Functional Differential ◽

Condensing Maps

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

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