
Journal of Convex Analysis 29 (2022), No. 3, 939974 Copyright Heldermann Verlag 2022 Periodic Problems for Doubly Nonlinear Evolution Equations Masahiro Koike ABeam Consulting Ltd., Tokyo, Japan koike.4.19@gmail.com Mitsuharu Otani Dept. of Applied Physics, School of Science and Engineering, Waseda University, Tokyo, Japan otani@waseda.jp Shun Uchida Department of Integrated Science and Technology, Faculty of Science and Technology,, Oita University, Oita City, Japan shunuchida@oitau.ac.jp We are concerned with the timeperiodic problem of some doubly nonlinear equations governed by differentials of two convex functionals over uniformly convex Banach spaces. G. Akagi and U. Stefanelli [Weighted energydissipation functionals for doubly nonlinear evolution, J. Funct. Analysis 260/9 (2011) 25412578] considered the Cauchy problem of the same equation via the socalled WED functional approach. The main purpose of this paper is to show the existence of the timeperiodic solution under the same growth conditions on functionals and differentials as those imposed in AkagiStefanelli [loc.cit]. Because of the difference in nature between the Cauchy problem and the periodic problem, we can not apply the WED functional approach directly, so we here adopt standard compactness methods with suitable approximation procedures. Keywords: Doubly nonlinear evolution equation, timeperiodic problem, subdifferential, pLaplacian, doubly nonlinear parabolic equation. MSC: 47J35; 35B10, 35K55, 35K92. [ Fulltextpdf (229 KB)] for subscribers only. 