Abstract
This paper is devoted to anti-periodic solutions for a class of implicit differential equations with nonmonotone perturbations. The main tools in our study will be the maximal monotone property of the derivative operator with anti-periodic conditions and a convergent approximation procedure.
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References
S. Aizicovici, M. McKibben and S. Reich, Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities, Nonlinear Anal., 43 (2001), 233–251.
S. Aizicovici and N. H. Pavel, Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space, J. Funct. Anal., 99 (1991), 387–408.
V. Barbu and A. Favini, Existence for implicit nonlinear differential equation, Nonlinear Analysis, TMA, 32 (1998), 33–40.
Yuqing Chen, Juan J. Nieto and D. O’Regan, Anti-periodic solutions for full nonlinear first-order differential equations, Mathematical and Computer Modelling, 46 (2007), 1183–1190.
Z. Denkowski, S. Migorski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications, Kluwer Academic/ Plenum Publishers (Boston, Dordrecht, London, New York, 2003).
A. Haraux, Anti-periodic solutions of some nonlinear evolution equations, Manuscripta Math., 63 (1989), 479–505.
W. Jager and L. Simon, On a system of quasilinear parabolic functional differential equations, Acta Math. Hungar., 112 (2006), 39–55.
Zhenhai Liu, Nonlinear evolution variational inequalities with nonmonotone perturbations, Nonlinear Analysis, TMA, 29 (1997), 1231–1236.
Zhenhai Liu and Zhang Shisheng, On the degree theory for multivalued (S+) type mappings, Appl. Math. Mech., 19 (1998), 1141–1149.
Zhenhai Liu, Existence for implicit differential equations with nonmonotone perturbations, Israel J. Math., 129 (2002), 363–372.
Zhenhai Liu, Anti-periodic solutions to nonlinear evolution equations, J. Funct. Anal., 258 (2010), 2026–2033.
H. Okochi, On the existence of periodic solutions to nonlinear abstract parabolic equations, J. Math. Soc. Japan, 40 (1988), 541–553.
H. Okochi, On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators, J. Funct. Anal., 91 (1990), 246–258.
L. Simon, On nonlinear hyperbolic functional differential equations, Math. Nachr., 217 (2000), 175–186.
L. Simon, On nonlinear systems consisting of different types of differential equations, Periodica Math. Hungar., 56 (2008), 143–156.
L. Simon, On a system with a singular parabolic equation, Folia FSN Univ. Masarykianae Brunensis, Math., 16 (2007), 149–156.
E. Zeidler, Nonlinear Functional Analysis and Its Applications, IIA and IIB, Springer (New York, 1990).
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Project supported by NNSF of China Grant No. 10971019 and NSF of Guangxi Grant No. 2010GXNSFA013114.
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Liu, J., Liu, Z. On the Existence of Anti-periodic Solutions for Implicit Differential Equations. Acta Math Hung 132, 294–305 (2011). https://doi.org/10.1007/s10474-010-0054-2
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DOI: https://doi.org/10.1007/s10474-010-0054-2