American Institute of Mathematical Sciences

Advanced
January  1996, 2(1): 53-63. doi: 10.3934/dcds.1996.2.53

Time dependent Volterra integral inclusions in Banach spaces

Sergiu Aizicovici 1, , Yimin Ding 1, and  N. S. Papageorgiou 2,

1. 

Department of Mathematics, Ohio University, Athens, Ohio 45701, United States, United States
2. 

Department of Mathematics, National Tech. University, Athens 15773, Greece

Received  April 1995 Published  October 1995

A nonlinear Volterra inclusion associated to a family of time-dependent $m$-accretive operators, perturbed by a multifunction, is considered in a Banach space. Existence results are established for both nonconvex and convex valued perturbations. The class of extremal solutions is also investigated.
Keywords: Volterra integral inclusion, compact evolution operator, $m$-accretive operator, mild (integral) solution..
Mathematics Subject Classification: 47Gx.
Citation: Sergiu Aizicovici, Yimin Ding, N. S. Papageorgiou. Time dependent Volterra integral inclusions in Banach spaces. Discrete and Continuous Dynamical Systems, 1996, 2 (1) : 53-63. doi: 10.3934/dcds.1996.2.53
[1]

Mario Ahues, Filomena D. d'Almeida, Alain Largillier, Paulo B. Vasconcelos. Defect correction for spectral computations for a singular integral operator. Communications on Pure and Applied Analysis, 2006, 5 (2) : 241-250. doi: 10.3934/cpaa.2006.5.241
[2]

Yixuan Wu, Yanzhi Zhang. Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 851-876. doi: 10.3934/dcdss.2022016
[3]

T. Diogo, P. Lima, M. Rebelo. Numerical solution of a nonlinear Abel type Volterra integral equation. Communications on Pure and Applied Analysis, 2006, 5 (2) : 277-288. doi: 10.3934/cpaa.2006.5.277
[4]

Antoine Hochart. An accretive operator approach to ergodic zero-sum stochastic games. Journal of Dynamics and Games, 2019, 6 (1) : 27-51. doi: 10.3934/jdg.2019003
[5]

Yazhou Han. Integral equations on compact CR manifolds. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2187-2204. doi: 10.3934/dcds.2020358
[6]

Lianwang Deng. Local integral manifolds for nonautonomous and ill-posed equations with sectorially dichotomous operator. Communications on Pure and Applied Analysis, 2020, 19 (1) : 145-174. doi: 10.3934/cpaa.2020009
[7]

Radjesvarane Alexandre, Lingbing He. Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$. Kinetic and Related Models, 2008, 1 (4) : 491-513. doi: 10.3934/krm.2008.1.491
[8]

Saima Rashid, Fahd Jarad, Zakia Hammouch. Some new bounds analogous to generalized proportional fractional integral operator with respect to another function. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3703-3718. doi: 10.3934/dcdss.2021020
[9]

M. R. Arias, R. Benítez. Properties of solutions for nonlinear Volterra integral equations. Conference Publications, 2003, 2003 (Special) : 42-47. doi: 10.3934/proc.2003.2003.42
[10]

Dorota Bors, Andrzej Skowron, Stanisław Walczak. Systems described by Volterra type integral operators. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2401-2416. doi: 10.3934/dcdsb.2014.19.2401
[11]

Hermann Brunner. On Volterra integral operators with highly oscillatory kernels. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 915-929. doi: 10.3934/dcds.2014.34.915
[12]

Saikat Mazumdar. Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary. Communications on Pure and Applied Analysis, 2017, 16 (1) : 311-330. doi: 10.3934/cpaa.2017015
[13]

Harry Crimmins. Stability of hyperbolic Oseledets splittings for quasi-compact operator cocycles. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2795-2857. doi: 10.3934/dcds.2022001
[14]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Mean-field backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1929-1967. doi: 10.3934/dcdsb.2013.18.1929
[15]

Eleonora Messina. Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation. Conference Publications, 2015, 2015 (special) : 826-834. doi: 10.3934/proc.2015.0826
[16]

Onur Alp İlhan. Solvability of some volterra type integral equations in hilbert space. Conference Publications, 2007, 2007 (Special) : 28-34. doi: 10.3934/proc.2007.2007.28
[17]

Tianxiao Wang, Yufeng Shi. Symmetrical solutions of backward stochastic Volterra integral equations and their applications. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 251-274. doi: 10.3934/dcdsb.2010.14.251
[18]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613
[19]

Z. K. Eshkuvatov, M. Kammuji, Bachok M. Taib, N. M. A. Nik Long. Effective approximation method for solving linear Fredholm-Volterra integral equations. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 77-88. doi: 10.3934/naco.2017004
[20]

Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3529-3539. doi: 10.3934/dcdss.2020432

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (88)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy