Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

2009 ◽  
Vol 142 (2) ◽  
pp. 267-273 ◽  
Author(s):  
Y. K. Chang ◽  
J. J. Nieto ◽  
W. S. Li
Keyword(s):  
Banach Spaces ◽  
Initial Conditions ◽  
Differential Systems ◽  
Nonlocal Initial Conditions

SEMILINEAR NONLOCAL PROBLEMS WITHOUT THE ASSUMPTIONS OF COMPACTNESS IN BANACH SPACES

2010 ◽  
Vol 08 (02) ◽  
pp. 211-225 ◽  
Author(s):  
XINGMEI XUE
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Differential System ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Problems ◽  
Hausdorff Measure Of Noncompactness ◽  
Nonlocal Initial Conditions

In this paper, we study the semilinear differential equations with nonlocal initial conditions in the separable Banach spaces. We derive conditions expressed in terms of the Hausdorff measure of noncompactness under which the mild solutions exit. For illustration, a partial integral differential system is worked out.

scholarly journals Functional differential equations with nonlocal initial conditions

1997 ◽  
Vol 10 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao
Keyword(s):  
Banach Spaces ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Cauchy Problems ◽  
Accretive Operators ◽  
Nonlocal Initial Conditions ◽  
Functional Differential

We study the existence, uniqueness, asymptotic properties, and continuous dependence upon data of solutions to a class of abstract nonlocal Cauchy problems. The approach we use is based on the theory of m-accretive operators and related evolution equations in Banach spaces.

scholarly journals One Sided Lipschitz Evolution Inclusions in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3265
Author(s):  
Ali N. A. Koam ◽  
Tzanko Donchev ◽  
Alina I. Lazu ◽  
Muhammad Rafaqat ◽  
Ali Ahmad
Keyword(s):  
Banach Spaces ◽  
Lipschitz Condition ◽  
Differential Inclusions ◽  
Initial Conditions ◽  
Lipschitz Constant ◽  
Evolution Inclusions ◽  
Nonlocal Initial Conditions ◽  
Limit Solution ◽  
The Right ◽  
Dissipative Differential Inclusions

Using the notion of limit solution, we study multivalued perturbations of m-dissipative differential inclusions with nonlocal initial conditions. These solutions enable us to work in general Banach spaces, in particular L1. The commonly used Lipschitz condition on the right-hand side is weakened to a one-sided Lipschitz one. No compactness assumptions are required. We consider the cases of an arbitrary one-sided Lipschitz condition and the case of a negative one-sided Lipschitz constant. Illustrative examples, which can be modifications of real models, are provided.

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