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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 68, 2019 - Issue 5
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Articles

Existence results of semilinear differential variational inequalities without compactness

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Pages 1017-1035 | Received 01 Oct 2018, Accepted 13 Jan 2019, Published online: 28 Jan 2019

References

  • Liu ZH, Zeng SD, Motreanu D. Evolutionary problems driven by variational inequalities. J Differ Equ. 2016;260:6787–6799. doi: 10.1016/j.jde.2016.01.012
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag; 1983.
  • Pang JS, Stewart DE. Differential variational inequalities. Math Program. 2008;113:345–424. doi: 10.1007/s10107-006-0052-x
  • Ke TD, Loi NV, Obukhovskii V. Decay solutions for a class of fractional differential variational inequalities. Fract Calc Appl Anal. 2015;18:531–553.
  • Li XS, Huang NJ, O'Regan D. A class of impulsive differential variational inequalities in finite dimensional spaces. J Franklin Inst. 2016;353:3151–3175. doi: 10.1016/j.jfranklin.2016.06.011
  • Li XS, Huang NJ, O'Regan D. Differential mixed variational inequalities in finite dimensional spaces. Nonlinear Anal. 2010;72:3875–3886. doi: 10.1016/j.na.2010.01.025
  • Loi NV. On two-parameter global bifurcation of periodic solutions to a class of differential variational inequalities. Nonlinear Anal. 2015;122:83–99. doi: 10.1016/j.na.2015.03.019
  • Liu ZH, Loi NV, Obukhovskii V. Existence and global bifurcation of periodic solutions to a class of differential variational inequalities. Internat J Bifur Chaos Appl Sci Engrg.. 2013;23:Article ID 1350125. doi: 10.1142/S0218127413501253
  • Liu ZH, Migórski S, Zeng SD. Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces. J Differ Equ. 2017;263:3989–4006. doi: 10.1016/j.jde.2017.05.010
  • Liu ZH, Motreanu D, Zeng SD. Nonlinear evolutionary systems driven by mixed variational inequalities and its applications. Nonlinear Anal: RWA. 2018;42:409–421. doi: 10.1016/j.nonrwa.2018.01.008
  • Liu ZH, Zeng SD. Differential variational inequalities in infinite dimensional Banach spaces. Acta Math Sci. 2017;37:26–32. doi: 10.1016/S0252-9602(16)30112-6
  • Lu L, Liu ZH, Obukhovskii V. Second order differential variational inequalities involving anti-periodic boundary value conditions, J Math Anal Appl (2019), https://doi.org/10.1016/j.jmaa.2018.12.072.
  • Migórski S, Zeng SD. Hyperbolic hemivariational inequalities controlled by evolution equations with application to adhesive contact model. Nonlinear Anal: RWA. 2018;43:121–143. doi: 10.1016/j.nonrwa.2018.02.008
  • Wang X, Tang GJ, Li XS, et al. Differential quasi-variational inequalities in finite dimensional spaces. Optimization. 2015;64:895–907. doi: 10.1080/02331934.2013.836646
  • Wang X, Qi YW, Tao CQ, et al. A class of delay differential variational inequalities. J Optim Theory Appl. 2017;172:56–69. doi: 10.1007/s10957-016-1002-2
  • Triggiani R. A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J Control Optim. 1977;15:407–411. doi: 10.1137/0315028
  • Triggiani R. Addendum a note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J Control Optim. 1980;18:98–99. doi: 10.1137/0318007
  • Benedetti I, Malaguti L, Taddei V. Semilinear differential inclusions via weak topologies. J Math Anal Appl. 2010;368:90–102. doi: 10.1016/j.jmaa.2010.03.002
  • Benedetti I, Malaguti L, Taddei V. Two-point b.v.p. for multivalued equations with weakly regular r.h.s.. Nonlinear Anal. 2011;74:3657–3670. doi: 10.1016/j.na.2011.02.046
  • Benedetti I, Obukhovskii V, Taddei V. Controllability for systems governed by semilinear evolution inclusions without compactness. Nonlinear Differ Equ Appl. 2014;21:795–812. doi: 10.1007/s00030-014-0267-0
  • Benedetti I, Väth M. Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces. Topol Methods Nonlinear Anal. 2016;48:613–636.
  • Zhou Y, Suganya S, Arjunan MM. Existence and controllability for impulsive evolution inclusions without compactness. J Dyn Control Syst. 2018;24:297–311. doi: 10.1007/s10883-017-9373-8
  • Zhou Y, Vijayakumar V, Murugesu R. Controllability for fractional evolution inclusions without compactness. Evol Equ Control Theory. 2015;4:507–524. doi: 10.3934/eect.2015.4.507
  • Kamemskii M, Obukhovskii V, Zecca P. Condensing multivalued maps and semilinear differential inclusions in Banach space. Berlin: Walter de Gruyter; 2001.
  • Migórski S, Ochal A, Sofonea M. Nonlinear inclusions and hemivariational inequalities. Models and Analysis of Contact Problems, Advances in Mechanics and Mathematics 26, New York: Springer; 2013.
  • Bochner S, Taylor AE. Linear functionals on certain spaces of abstractly-valued functions. Ann Math. 1938;39:913–944. doi: 10.2307/1968472
  • Costea N, Lupu C. On a class of variational-hemivariational inequalities involving set valued mappings. Adv Pure Appl Math. 2010;1:233–246. doi: 10.1515/apam.2010.014
  • Diestel J, Ruess WM, Schachermayer W. Weak compactness in L1(μ,X). Proc Amer Math Soc. 1993;118:447–453.
  • Tang GJ, Huang NJ. Existence theorems of the variational-hemivariational inequalities. J Glob Optim. 2013;56:605–622. doi: 10.1007/s10898-012-9884-5
  • Glicksberg IL. A further generalization of the Kakutani fixed theorem with application to Nash equilibrium points. Proc Amer Math Soc. 1952;3:170–174.
  • Krein SG. Linear differential equations in Banach spaces. Providence: American Mathematical Society; 1971.
  • Dunford N, Schwartz JT. Linear operators. New York: Wiley; 1988.

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