scholarly journals Solutions of Cauchy and periodic problems for evolution inclusions with multi-valued wλ0-pseudomonotone maps

2010 ◽  
Vol 249 (6) ◽  
pp. 1258-1287 ◽  
Author(s):  
P.O. Kasyanov ◽  
V.S. Mel'nik ◽  
S. Toscano
Keyword(s):  
Evolution Inclusions ◽  
Periodic Problems ◽  
Pseudomonotone Maps

SET-VALUED PSEUDOMONOTONE MAPS AND DEGENERATE EVOLUTION INCLUSIONS

1999 ◽  
Vol 01 (01) ◽  
pp. 87-123 ◽  
Author(s):  
KENNETH L. KUTTLER ◽  
MEIR SHILLOR
Keyword(s):  
Weak Solution ◽  
Friction Coefficient ◽  
Frictional Contact ◽  
Contact Problems ◽  
Pseudomonotone Operator ◽  
Unique Weak Solution ◽  
Dynamical Models ◽  
Evolution Inclusions ◽  
Theory Of Evolution ◽  
Pseudomonotone Maps

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are [Formula: see text] where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems.We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution.This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.

scholarly journals Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

On evolution inclusions with nonconvex valued orientor fields

1996 ◽  
Vol 26 (1) ◽  
pp. 1-8 ◽  
Author(s):  
D. Kravvaritis ◽  
G. Pantelidis
Keyword(s):  
Evolution Inclusions ◽  
Orientor Fields

Optimal control of evolution inclusions

2005 ◽  
Vol 63 (5-7) ◽  
pp. 775-784 ◽  
Author(s):  
Boris S. Mordukhovich
Keyword(s):  
Optimal Control ◽  
Evolution Inclusions

Periodic Problems with the Scalar p-Laplacian Resonant at any Eigenvalue via Critical Point Methods

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Donal O’ Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Morse Theory ◽  
Critical Point Theory ◽  
Smooth Solution ◽  
Point Theory ◽  
Reaction Term ◽  
Variational Techniques ◽  
Periodic Problems

AbstractWe consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

scholarly journals Existence for Singular Periodic Problems: A Survey of Recent Results

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Jifeng Chu ◽  
Juntao Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Differential Systems ◽  
Singular Differential Equations ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

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