Clarke, Frank H.; Ekeland, I. Nonlinear oscillations and boundary value problems for Hamiltonian systems. (English) Zbl 0514.34032 Arch. Ration. Mech. Anal. 78, 315-333 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 42 Documents MSC: 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:nonlinear oscillations; nonautonomous Hamiltonian system; parametric oscillations; conjugate convex function; variational principle; Hamiltonian inclusion; subdifferentials PDF BibTeX XML Cite \textit{F. H. Clarke} and \textit{I. Ekeland}, Arch. Ration. Mech. Anal. 78, 315--333 (1982; Zbl 0514.34032) Full Text: DOI OpenURL References: [1] H. Amann & E. Zehnder, Multiple solutions for a class of nonresonance problems and applications to differential equations, to appear. · Zbl 0452.47077 [2] J. P. Aubin & I. Ekeland, Second-order evolution equations associated with convex Hamiltonians, Cahiers Mathématiques de la Décision, No. 7825, to appear. [3] F. H. Clarke, The Euler-Lagrange differential inclusion, J. Differential Equations 19 (1975), 80–90. · Zbl 0323.49021 [4] F. H. Clarke, Periodic solutions to Hamiltonian inclusions, J. Differential Equations 40 (1981) 1–6. · Zbl 0461.34030 [5] F. H. Clarke, Multiple integrals of Lipschitz functions in the calculus of variations, Proc. Amer. Math. Soc. 64 (1977), 260–264. · Zbl 0411.49015 [6] F. H. Clarke & I. Ekeland, Hamiltonian trajectories having prescribed minimal period, Comm. Pure Applied Math. 33 (1980), 103–116. · Zbl 0428.70029 [7] I. Ekeland, Periodic Hamiltonian trajectories and a theorem of Rabinowitz, J. Differential Equations 34 (1979), 523–534. · Zbl 0446.70019 [8] I. Ekeland & J. M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Annals of Math. 112 (1980) 283–319. · Zbl 0449.70014 [9] I. Ekeland & R. Temam, ”Convex Analysis and Variational Problems,” North-Holland (1976). · Zbl 0322.90046 [10] P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Applied Math. 31 (1978), 157–184. · Zbl 0369.70017 [11] P. H. Rabinowitx, A variational method for finding periodic solutions of differential equations, in ”Nonlinear Evolution Equations,” edited by M. Crandall, Academic Press (1980). [12] R. T. Rockafellar, ”Convex Analysis,” Princeton University Press (1970). · Zbl 0193.18401 [13] A. Weinstein, Periodic orbits for convex Hamiltonian systems, Annals of Math. 108 (1978), 507–518. · Zbl 0403.58001 [14] V. Benci & P. Rabinowitz, ”Critical point theorems for indefinite functional,” Inventiones Math., 52 (1979), 241–273. · Zbl 0465.49006 [15] H. Brezis & L. Nirenberg, ”Characterization of the range of some nonlinear operators and applications to boundary value problems,” Annali Scuola Norm. Sup. Pisa, 5 (1978), 225–326. [16] H. Brezis & A. Bahri, ”Periodic solutions of a nonlinear wave equation,” to appear. [17] J. M. Coron, ”Resolution de l’équation Au+Bu=f, ou A est linéaire autoadjoint et B dérivé d’un potentiel convexe,” to appear. [18] F. H. Clarke, ”Solutions périodiques des équations hamiltoniennes”, C. R. Acad. Sci. Paris 287 (1978), 951–952. · Zbl 0422.35005 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.