scholarly journals Measures of weak noncompactness in Banach spaces

2009 ◽  
Vol 156 (7) ◽  
pp. 1412-1421 ◽  
Author(s):  
C. Angosto ◽  
B. Cascales
Keyword(s):  
Banach Spaces ◽  
Measures Of Weak Noncompactness

scholarly journals Weak solutions for nonlinear fractional differential equation with fractional separated boundary conditions in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1117-1125 ◽  
Author(s):  
Hamza Rebai ◽  
Djamila Seba
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Weak Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Weak Solutions ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Measures Of Weak Noncompactness

This paper deals with nonlinear fractional differential equation with fractional separated boundary conditions. We investigate the existence of weak solutions in Banach spaces. To obtain such result we apply an appropriate fixed point theorem and the technique of measures of weak noncompactness. An example illustrating the theory is given.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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