Solutions of semi-linear stochastic evolution integro-differential inclusions with Poisson jumps and non-local initial conditions

References

• H.M. Ahmed, Sobolev-type fractional stochastic integrodifferential equations with nonlocal conditions in Hilbert space, J. Theor. Probab. 30 (2017), pp. 771–783.
   Web of Science ®Google Scholar
• M. Benchohra, J. Henderson, and S.K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Coporation, New York, 2006.
   Google Scholar
• G.L. Cao, K. He, and X. Zhang, Successive approximation of infinite dimensinal SDES with jump, Stoch. Dynam. 5 (2005), pp. 609–619.
   Google Scholar
• R.M. Christensen, The Theory of Linear Viscoelasticity: An Introduction, Academic Press, New York, 1982.
   Google Scholar
• K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), pp. 630–637.
   Web of Science ®Google Scholar
• M. Dieye, M.A. Diop, and K. Ezzinbi, On exponential stability of mild solutions for some stochastic partial integrodifferential equations, Stat. Prob. Lett. 123 (2017), pp. 61–76.
   Web of Science ®Google Scholar
• M. Dieye, M.A. Diop, and K. Ezzinbi, Optimal feedback control law for some stochastic integrodifferential equations on Hilbert spaces, European J. Control 37 37 (2017), pp. 54–62.
   Web of Science ®Google Scholar
• S. Djebali, L. Górniewicz, and A. Ouahab, Solution Sets for Differential Equations and Inclusions, De Gruyter, Berlin, 2013.
   Google Scholar
• P. Duan and Y. Ren, Solvability and stability for neutral stochastic integro-differential equations driven by fractional Brownian motion with impulses, Mediterr. J. Math. 15 (2018). Art. 207.
   Web of Science ®Google Scholar
• K. Ezzinbi and S. Ghnimi, Exiseence and regularity of solutions for neutral partial functional integrodifferential equations, Nonlinear Anal: RWA 11 (2010), pp. 2335–244.
   Google Scholar
• K. Ezzinbi and S. Ghnimi, Existence and regularity of solutions for some partial integrodifferential equations involving the nonlocal conditions, Numer. Funct. Anal. Optim. 40 (2019), pp. 1532–1549.
   Web of Science ®Google Scholar
• L. Górniewicz and M. Lassonde, Approximation and fixed points for compositions of Rδ-maps, Topol. Appl. 55 (1994), pp. 239–250.
   Web of Science ®Google Scholar
• J.R. Graef, J. Henderson, and A. Ouahab, Impulsive Differential Inclusions: A Fixed Point Approach, Walter de Gruyter, Berlin, 2013.
   Google Scholar
• R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 (1982), pp. 333–349.
   Web of Science ®Google Scholar
• M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multi-valued Maps and Semilinear Differential Inclusions in Banach Spaces, Walter de Gruyter, New York, 2001.
   Google Scholar
• M. Kisielewicz, Stochastic Differential Inclusions and Applications, Springer, New York, 2013.
   Google Scholar
• J.H. Liu and K. Ezzinbi, Non-autonomous integrodifferential equations with nonlocal conditions, J. Integral Equ. Appl. 15 (2003), pp. 79–93.
   Google Scholar
• Q. Lü and X. Zhang, A concise introduction to control theory for stochastic partial differential equations, to appear in Math. Control Relat. Fields, Available at https://doi.org/http://doi.org/10.3934/mcrf.2021020.
   Google Scholar
• M.A. Meyers and K.K. Chawla, Mechanical behavior of materials, Cambridge University Press, Cambridge, 2009.
   Google Scholar
• P. Muthukumar and K. Thiagu, Existence of solutions and approximate controllability of fractional nonlocal neutral impulsive stochastic differential equations of order 1<q<2 with infinite delay and Poisson jumps, J. Dym. Control Syst. 23 (2017), pp. 213–235.
   Web of Science ®Google Scholar
• D. O'Regan, Fixed point theorems for weakly sequentially closed maps, Arch. Math. 36 (2000), pp. 61–70.
   Google Scholar
• R. Ravi Kumar, Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), pp. 352–362.
   Web of Science ®Google Scholar
• R. Ravi Kumar, Regularity of solutions of evolution integrodifferential equations with deviating argument, Appl. Math. Comput. 217 (2011), pp. 9111–9121.
   Web of Science ®Google Scholar
• Y. Ren, Q. Zhou, and L. Chen, Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with Poisson jumps and infinite delay, J. Optim. Theory Appl. 149 (2011), pp. 315–331.
   Web of Science ®Google Scholar
• Y. Ren and R. Sakthivel, Existence, uniqueness, and stability of mild solutions for second-order neutral stochastic evolution equations with infinite delay and Poisson jumps, J. Math. Phys. 53 (2012), pp. 835–863.
   Web of Science ®Google Scholar
• R. Sakthivel and Y. Ren, Complete controllability of stochastic evolution equations with jumps, Rep. Math. Phys. 68 (2011), pp. 163–174.
   Web of Science ®Google Scholar
• R. Sakthivel and Y. Ren, Exponential stability of second-order stochastic evolution equations with Poisson jumps, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012), pp. 4517–4523.
   Web of Science ®Google Scholar
• P. Thamilalagan and P. Balasubramaniam, The solvability and optimal controls for fractional stochastic differential equations driven by Poisson jumps via resolvent operators, Appl. Math. Optim. 77 (2018), pp. 443–462.
   Web of Science ®Google Scholar
• T. Taniguchi and J.W. Luo, The existence and asymptotic behaviour of mild solutions to stochastic evolution equations with infinite delays driven by Poisson jumps, Stoch. Dyn. 9 (2009), pp. 217–229.
   Web of Science ®Google Scholar
• A.A. Tolstonogov, Differential Inclusions in a Banach Space, Kluwer Academic, Dordrecht, 2000.
   Google Scholar
• J.R. Wang, A. Ibrahim, and M. Feckan, Nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces, Commun. Nonlinear Sci. Numer. Simul. 27 (2015), pp. 281–293.
   Web of Science ®Google Scholar
• R.N. Wang, K. Ezzinbi, and P.X. Zhu, Non-autonomous impulsive Cauchy problems of parabolic type involving nonlocal initial conditions, J Integral Equ. Appl. 26 (201), pp. 275–299.
   Google Scholar
• R.N. Wang, P.X. Zhu and Q.H. Ma, Multi-valued nonlinear perturbations of time fractional evolution equations in Banach spaces, Nonlinear Dyn. 80 (2015), pp. 1745–1759.
   Web of Science ®Google Scholar
• M. Yang and Q.R. Wang, Existence of mild soltions for a class of Hilfer fractional evolution equations with nonlocal conditions, Fract. Calc. Appl. Anal. 20 (2017), pp. 679–705.
   Web of Science ®Google Scholar
• Z.H. Zhao and Y.K. Chang, Topological properties of solution sets for Sobolev-type fractional stochastic differential inclusions with Poisson jumps, Appl. Anal. 99 (2020), pp. 1373–1401.
   Web of Science ®Google Scholar
• Y. Zhou, R.N. Wang, and L. Peng, Topological Structure of the Solution Set for Evolution Inclusions, Springer, Singapore, 2017.
   Google Scholar
• Y. Zhou, L. Peng and B. Ahmad, Topological properties of solution sets for stochastic evolution inclusions, Stoch. Anal. Appl. 36 (2018), pp. 114–137.
   Web of Science ®Google Scholar