Anti-periodic solutions to a parabolic hemivariational inequality. (English) Zbl 1249.35190

Summary: In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form \(b(u)\), where \(b\in L^{\infty }_{\text{loc}}(\mathbb {R}).\) Extending \(b\) to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.


35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
35B10 Periodic solutions to PDEs
Full Text: EuDML Link


[1] Aizicovici S., Mckibben M., Reich S.: Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal. 43 (2001), 233-251 · 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 (1991), 387-408 · Zbl 0743.34067
[3] Aizicovici S., Reich S.: Anti-periodic solutions to a class of non-monotone evolution equations. Discrete Contin. Dynam. Systems. 5 (1999), 35-42 · Zbl 0961.34044
[4] Barbu V.: Nonlinear Semigroups and Differential Equations in Banach Spacess. Noordhoff, Leyden 1976
[5] Miettinen M.: A parabolic hemivariational inequality. Nonlinear Anal. 26 (1996), 725-734 · Zbl 0858.35072
[6] Miettinen M., Panagiotopoulos P. D.: On parabolic hemivariational inequalities and applications. Nonlinear Anal. 35 (1999), 885-915 · Zbl 0923.35089
[7] Nakao M.: Existence of an anti-periodic solution for the quasilinear wave equation with viscosity. J. Math. Anal. Appl. 204 (1996), 754-764 · Zbl 0873.35051
[8] Nakao M., Okochi H.: Anti-periodic solutions for \(u_{tt}-(\sigma (u_x))_x-u_{xxt}=f(x,t)\). J. Math. Anal. Appl. 197 (1996), 796-809 · Zbl 0863.35066
[9] Okochi H.: On the existence of periodic solutions to nonlinear abstract parabolic equations. J. Math. Soc. Japan 40 (1988), 541-553 · Zbl 0679.35046
[10] Panatiotopoulos P. D.: Nonconvex superpotentials in the sense of F. H. Clarke and applications. Mech. Res. Comm. 8 (1981), 335-340
[11] Rauch J.: Discontinuous semilinear differential equations and multiple valued maps. Proc. Amer. Math. Soc. 64 (1977), 277-282 · Zbl 0413.35031
[12] Showalter R. E.: Monotone operators in Banach space and nonlinear partial differential equations. Mathematical Surveys Monographs 49 (1996) · Zbl 0870.35004
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.