Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls on Banach spaces

A class of second-order nonlinear impulsive integro-differential equations of mixed type whose principal part is given by time-varying generating operators in fractional power spaces is considered. We introduce the reasonable PC-α-mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove its existence. The existence of optimal controls for a Lagrange problem of systems governed by second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.

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

Nonlinear Analysis ◽

10.1016/j.na.2006.08.033 ◽

2007 ◽

Vol 67 (8) ◽

pp. 2335-2349 ◽

Cited By ~ 14

Author(s):

Xinguang Zhang ◽

Lishan Liu ◽

Yonghong Wu

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Mixed Type ◽

Global Solutions ◽

Second Order ◽

Equations Of Mixed Type

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The unique solution of boundary value problems for nonlinear second-order integral–differential equations of mixed type in Banach spaces

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2007.04.018 ◽

2007 ◽

Vol 54 (9-10) ◽

pp. 1293-1301 ◽

Cited By ~ 7

Author(s):

Zenggui Wang ◽

Lishan Liu ◽

Yonghong Wu

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Banach Spaces ◽

Unique Solution ◽

Mixed Type ◽

Boundary Value ◽

Second Order ◽

Equations Of Mixed Type ◽

Integral Differential Equations

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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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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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Extreme solutions of nonlinear, second order integro-differential equations in Banach spaces

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953395000281 ◽

1995 ◽

Vol 8 (3) ◽

pp. 319-329 ◽

Cited By ~ 7

Author(s):

Dajun Guo

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Mixed Type ◽

Second Order ◽

New Method ◽

Comparison Result ◽

Equations Of Mixed Type ◽

Maximal And Minimal Solutions ◽

Extreme Solutions

After establishing a comparison result by means of a new method, we obtain the existence of maximal and minimal solutions for nonlinear, second order integro-differential equations of mixed type in Banach spaces.

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