Anti-periodic solutions to nonlinear evolution equations. (English) Zbl 1184.35184

Summary: We deal with anti-periodic problems for nonlinear evolution equations with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.


35K90 Abstract parabolic equations
35K55 Nonlinear parabolic equations
47H05 Monotone operators and generalizations
35B10 Periodic solutions to PDEs
Full Text: DOI


[1] Aizicovici, S.; McKibben, M.; Reich, S., Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities, Nonlinear anal., 43, 233-251, (2001) · Zbl 0977.34061
[2] Aizicovici, S.; Pavel, N.H., Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space, J. funct. anal., 99, 387-408, (1991) · Zbl 0743.34067
[3] Barbu, V., Nonlinear semigroup and differential equations in Banach spaces, (1976), Noordhoff Leyden
[4] Chen, Yuqing, Anti-periodic solutions for semilinear evolution equations, J. math. anal. appl., 315, 337-348, (2006) · Zbl 1100.34046
[5] Chen, Yuqing; Nieto, Juan J.; O’Regan, Donal, Anti-periodic solutions for full nonlinear first-order differential equations, Math. comput. modelling, 46, 1183-1190, (2007) · Zbl 1142.34313
[6] Haraux, A., Anti-periodic solutions of some nonlinear evolution equations, Manuscripta math., 63, 479-505, (1989) · Zbl 0684.35010
[7] Liu, Zhenhai, Nonlinear evolution variational inequalities with nonmonotone perturbations, Nonlinear anal., 29, 1231-1236, (1997) · Zbl 0902.47057
[8] Liu, Zhenhai, Existence for implicit differential equations with nonmonotone perturbations, Israel J. math., 129, 363-372, (2002) · Zbl 1012.34055
[9] Okochi, H., On the existence of periodic solutions to nonlinear abstract parabolic equations, J. math. soc. Japan, 40, 541-553, (1988) · Zbl 0679.35046
[10] Okochi, H., On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators, J. funct. anal., 91, 246-258, (1990) · Zbl 0735.35071
[11] Okochi, H., On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains, Nonlinear anal., 14, 771-783, (1990) · Zbl 0715.35091
[12] Zeidler, E., Nonlinear functional analysis and its applications, vols. IIA and IIB, (1990), Springer New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.