Nonlinear periodic system with unilateral constraints

Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu



We consider a general periodic system driven by a nonlinear, nonhomogeneous differential operator, with a maximal monotone term which is not defined everywhere. Using a topological approach based on Leray-Schauder alternative principle, we show the existence of a periodic solution.


Maximal monotone map; periodic solution; resolvent; Yosida approximation; chain rule

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S. Aizicovici, N.S. Papageorgiou and V. Staicu, Nodal and multiple solutions for nonlinear periodic problems with competing nonlinearities, Commun. Contemp. Math. 15 (2013), no. 3, 1350001–1350030.

S. Aizicovici, N.S. Papageorgiou and V. Staicu, Nonlinear, nonconvex second order multivalued systems with maximal monotone terms, Pure Appl. Funct. Anal. 2 (2017), 553–574.

L. Gasinski and N.S. Papageorgiou, Nonlinear Analysis, Chapman & Hall/CRC Press, Boca Raton, 2006.

P. Hartman, On boundary value problems for systems of ordinary nonlinear second order differential equations, Trans. Amer. Math. Soc. 96 (1960), 493–509.

H.W. Knobloch, On the existence of periodic solutions for second order vector differential equations, J. Differential Equations 9 (1971), 67–85.

H.W. Knobloch and K. Schmitt, Nonlinear boundary value problems for systems of differential equations, Proc. Roy. Soc. Edinburgh Sect. A 78 (1977), 139–159.

R. Manasevich and J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations 145 (1998), 367–393.

M. Marcus and V. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces, Arch. Ration. Mech. Anal. 45 (1972), 294–320.

J. Mawhin, Some boundary value problems for Harman-type perturbations of the ordinary vector p-Laplacian, Nonlinear Anal. 40 (2000), 497–503.

I. Vrabie, Compactness Methods for Nonlinear Evolutions, Longman Scientific and Technical, Harlow, Essex, 1987.


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