Rothe's method and weak solutions of perturbed evolution equations in reflexive Banach spaces

1976 ◽  
Vol 219 (2) ◽  
pp. 159-166 ◽  
Author(s):  
A. G. Kartsatos ◽  
W. R. Zigler
Keyword(s):  
Banach Spaces ◽  
Weak Solutions ◽  
Evolution Equations ◽  
Reflexive Banach Spaces ◽  
Rothe's Method ◽  
Rothe’S Method

Quasi-linear evolution equations in non-reflexive banach spaces, I

1981 ◽  
Vol 5 (4) ◽  
pp. 411-421
Author(s):  
Mieczyslaw Altman
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Reflexive Banach Spaces ◽  
Linear Evolution ◽  
Linear Evolution Equations

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

scholarly journals Nonzero solutions for a class of set-valued variational inequalities in reflexive Banach spaces

2008 ◽  
Vol 56 (1) ◽  
pp. 233-241
Author(s):  
Jianghua Fan ◽  
Wenhong Wei
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Reflexive Banach Spaces
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