$M$-periodic problem of order $2k$
Copyright policy )$M$-periodic problem of order $2k$
The author gives sufficient conditions for the existence of solutions to some general matrix-periodic problems of higher even order, which have a variational structure. A key tool in the proofs is a generalization of the Du Bois-Reymond lemma for periodic functions of order one, which was proved by the author in a previous work [Gȩba, Kazimierz (ed.) et al., Topology in nonlinear analysis. Banach Cent. Publ. 35, 221-236 (1996; Zbl 0868.49015)].
Du Bois-Reymond lemma, Methods involving semicontinuity and convergence; relaxation, periodic functions, existence, variational methods, matrix-periodic problems, Periodic solutions to ordinary differential equations
Du Bois-Reymond lemma, Methods involving semicontinuity and convergence; relaxation, periodic functions, existence, variational methods, matrix-periodic problems, Periodic solutions to ordinary differential equations
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