scholarly journals On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces

2016 ◽  
Vol 09 (06) ◽  
pp. 3879-3891 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Inclusion Problems

scholarly journals Well-posedness of Hemivariational Inequalities and Inclusion Problems

2011 ◽  
Vol 15 (3) ◽  
pp. 1261-1276 ◽  
Author(s):  
Yi-bin Xiao ◽  
Nan-jing Huang ◽  
Mu-Ming Wong
Keyword(s):  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Inclusion Problems

scholarly journals Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

2017 ◽  
Vol 48 (4) ◽  
pp. 345-364 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yung-Yih Lur ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Minimization Problem ◽  
Hemivariational Inequality ◽  
Inclusion Problem ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Reflexive Banach Spaces ◽  
Mild Conditions ◽  
Well Posed

In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces. We establish some metric characterizations for the $\alpha$-well-posed generalized variational-hemivariational inequality and give some conditions under which the generalized variational-hemivariational inequality is strongly $\alpha$-well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the $\alpha$-well-posedness of the generalized variational-hemivariational inequality and the $\alpha$-well-posedness of the corresponding inclusion problem.

scholarly journals Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces

2017 ◽  
Vol 10 (08) ◽  
pp. 4318-4336 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Time Dependent ◽  
Hemivariational Inequalities ◽  
Well Posedness

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 Well-Posedness of Minimal Time Problems with Constant Dynamics in Banach Spaces

2010 ◽  
Vol 18 (3-4) ◽  
pp. 349-372 ◽  
Author(s):  
Giovanni Colombo ◽  
Vladimir V. Goncharov ◽  
Boris S. Mordukhovich
Keyword(s):  
Banach Spaces ◽  
Well Posedness ◽  
Minimal Time
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