Controllability for a class of second-order evolution differential inclusions without compactness

References

• Arthi G , Balachandran K . Controllability of second-order impulsive evolution systems with infinite delay. Nonlinear Anal Hybrid Syst. 2014;11:139–153.
   Web of Science ®Google Scholar
• Arthi G , Park JH , Jung HY . Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay. Appl Math Comput. 2014;248:328–341.
   Web of Science ®Google Scholar
• Chang YK , Li WT . Controllability of functional integro-differential inclusions with an unbounded delay. J Optim Theory Appl. 2007;132(1):125–142.
   Web of Science ®Google Scholar
• Chang YK , Anguraj A , Mallika Arjunan M . Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces. Chaos Solitons Fractals. 2009;39(4):1864–1876.
   Web of Science ®Google Scholar
• Chang YK . Controllability of impulsive functional differential systems with infinite delay in Banach spaces. Chaos Solitons Fractals. 2007;33(5):1601–1609.
   Web of Science ®Google Scholar
• Ke TD . Controllability for semilinear functional differential equations without uniqueness. Electron J Differ Equ. 2014;36:1–15.
   Google Scholar
• Machado JA , Ravichandran C , Rivero M , et al . Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions. Fixed Point Theory Appl. 2013;66(1):1–16.
   Google Scholar
• Mahmudov NI , Vijayakumar V , Murugesu R . Approximate controllability of second-order evolution differential inclusions in Hilbert spaces. Mediterr J Math. 2016;13(5):3433–3454.
   Web of Science ®Google Scholar
• Naito K . Controllability of semilinear system dominated by the linear part. SIAM J Control Optim. 1987;25:715–722.
   Web of Science ®Google Scholar
• Obukhovski V , Zecca P . Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup. Nonlinear Anal. 2009;70:3424–3436.
   Web of Science ®Google Scholar
• Ravichandran C , Trujillo JJ . Controllability of impulsive fractional functional integro-differential equations in Banach spaces. J Funct Spaces. 2013;2013(1):1–8. Article ID-812501.
   Google Scholar
• Ravichandran C , Baleanu D . On the controllability of fractional functional integro-differential systems with an infinite delay in Banach spaces. Adv Differ Equ. 2013;291:1–13.
   Google Scholar
• Vijayakumar V , Ravichandran C , Murugesu R . Approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay. Nonlinear Stud. 2013;20(4):511–530.
   Google Scholar
• Vijayakumar V , Murugesu R , Tamil Selvan M . Controllability for a class of second order functional evolution differential equations without uniqueness. IMA J Math Control Inform. 2017:1–22. DOI:10.1093/imamci/dnx048
   Google Scholar
• Vijayakumar V . Approximate controllability results for abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces. IMA J Math Control Inform. 2016:1–18. DOI:10.1093/imamci/dnw049
   Web of Science ®Google Scholar
• Vijayakumar V . Approximate controllability results for analytic resolvent integro-differential inclusions in Hilbert spaces. Int J Control. 2018;91(1):204–214.
   Web of Science ®Google Scholar
• Vijayakumar V . Approximate controllability results for impulsive neutral differential inclusions of Sobolev-type with infinite delay. Int J Control. 2017:1–21. DOI:10.1080/00207179.2017.1346300
   Web of Science ®Google Scholar
• Wang J , Zhou Y . Existence and controllability results for fractional semilinear differential inclusions. Nonlinear Anal Real World Appl. 2011;12:3642–3653.
   Web of Science ®Google Scholar
• Zhou Y , Vijayakumar V , Murugesu R . Controllability for fractional evolution inclusions without compactness. Evol Equ Control Theory. 2015;4(4):507–524.
   Web of Science ®Google Scholar
• Benedetti I , Obukhovskii V , Taddei V . Controllability for systems governed by semilinear evolution inclusions without compactness. Nonlinear Differ Equ Appl. 2014;21:795–812.
   Web of Science ®Google Scholar
• Zhou Y , Suganya S , Mallika Arjunan M . Existence and controllability for impulsive evolution inclusions without compactness. J Dyn Control Syst. 2017:1–15. DOI:10.1007/s10883-017-9373-8
   Web of Science ®Google Scholar
• Batty CJK , Chill R , Srivastava S . Maximal regularity for second order non-autonomous Cauchy problems. Stud Math. 2008;189:205–223.
   Web of Science ®Google Scholar
• Faraci F , Iannizzotto A . A multiplicity theorem for a perturbed second-order non-autonomous system. Proc Edinburgh Math Soc. 2006;49:267–275.
   Web of Science ®Google Scholar
• Henríquez HR . Existence of solutions of non-autonomous second order functional differential equations with infinite delay. Nonlinear Anal Theory Methods Appl. 2011;74:3333–3352.
   Web of Science ®Google Scholar
• Kozak M . A fundamental solution of a second order differential equation in a Banach space. Univ Iagel Acta Math. 1995;32:275–289.
   Google Scholar
• Travis CC , Webb GF . Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston J Math. 1977;3(4):555–567.
   Google Scholar
• Travis CC , Webb GF . Cosine families and abstract nonlinear second order differential equations. Acta Math Acad Sci Hung. 1978;32:76–96.
   Web of Science ®Google Scholar
• Kisyński J . On cosine operator functions and one parameter group of operators. Stud Math. 1972;49:93–105.
   Web of Science ®Google Scholar
• Serizawa H , Watanabe M . Time-dependent perturbation for cosine families in Banach spaces. Houston J Math. 1986;12:579–586.
   Web of Science ®Google Scholar
• Bochner S , Taylor AE . Linear functionals on certain spaces of abstractly valued functions. Ann Math. 1938;39:913–944.
   Google Scholar
• Fan K . Fixed-point and minimax theorems in locally convex topological linear spaces. Proc Nat Acad Sci USA. 1952;38(2):121–126.
   PubMed Web of Science ®Google Scholar
• Glicksberg IL . A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc Am Math Soc. 1952;3(1):170–174.
   Web of Science ®Google Scholar
• Kantorovich LV , Akilov GP . Functional analysis. Oxford: Pergamon Press; 1982.
   Google Scholar
• Dunford N , Schwartz JT . Linear operators. New York (NY): Wiley; 1988.
   Google Scholar
• Pettis BJ . On the integration in vector spaces. Trans Am Math Soc. 1938;44:277–304.
   Google Scholar
• Brezis H . Analyse Fonctionelle, Théorie et Applications. Paris: Masson Editeur; 1983.
   Google Scholar
• Byszewski L . Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J Math Anal Appl. 1991;162:494–505.
   Web of Science ®Google Scholar
• Byszewski L , Akca H . On a mild solution of a semilinear functional-differential evolution nonlocal problem. J Appl Math Stoch Anal. 1997;10(3):265–271.
   Google Scholar
• Byszewski L , Lakshmikantham V . Theorem about the existence and uniqueness of solutions of a nonlocal Cauchy problem in a Banach space. Appl Anal. 1990;40:11–19.
   Google Scholar
• Fu X , Ezzinbi K . Existence of solutions for neutral functional differential evolution equations with nonlocal conditions. Nonlinear Anal. 2003;54:215–227.
   Web of Science ®Google Scholar
• Mahmudov NI , Murugesu R , Ravichandran C , et al . Approximate controllability results for fractional semilinear integro-differential inclusions in Hilbert spaces. Results Math. 2017;71(1):45–61.
   Web of Science ®Google Scholar
• Sivasankaran S , Mallika Arjunan M , Vijayakumar V . Existence of global solutions for impulsive functional differential equations with nonlocal conditions. J Nonlinear Sci Appl. 2011;4(2):102–114.
   Google Scholar
• Sivasankaran S , Mallika Arjunan M , Vijayakumar V . Existence of global solutions for second order impulsive abstract partial differential equations. Nonlinear Anal Theory Methods Appl. 2011;74(17):6747–6757.
   Web of Science ®Google Scholar