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Bibliography
Aubry, S., & P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions, Physica 8D (1983), 381–422.
Artstein, Z., & A. Leizarowitz, Tracking periodic signals with overtaking criterion, IEEE Trans. on Autom. Control AC 30 (1985), 1122–1126.
Brock, W. A., A. Haurie, On existence of overtaking optimal trajectories over an infinite time horizon, Math. Op. Res. 1 (1976), 337–346.
Carlson, D., On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals, J. Optim. Thy. Appl. 49 (1986), 207–225.
Coleman, B. D., Necking and drawing in polymeric fibers under tension, Arch. Rational Mech. Anal. 83 (1983), 115–137.
Coleman, B. D., On the cold drawing of polymers, Comp. & Maths. with Appl. 11 (1985), 35–65.
Chou, W., & R. J. Duffin, An additive eigenvalue problem of physics related to linear programming, Adv. in Appl. Math. 8 (1987), 486–498.
Cahn, J. W., & J. E. Milliard, Free energy of a nonuniform system. I, Inter-facial free energy. J. Chem. Physics 28 (1958), 258–267.
Carr, J., M. E., Gurtin & M. Slemrod, Structural phase transitions on a finite interval, Arch. Rational Mech. Anal. 86 (1984), 317–351.
Giaquinta, M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies # 105, Princeton U. Press, Princeton 1983.
Griffiths, R. B., & W. Chou, Effective potentials: a new approach and new results for one-dimensional systems with competing length scales, Phys. Rev. Letters 56 (1986), 1929–1931.
Leizarowitz, A., Infinite horizon autonomous systems with unbounded cost, Appl. Math. and Opt. 13 (1985), 19–43.
Lions, J. L., & E. Magenes, Non-homogeneous boundary value problems and Applications I, Grundlehren # 181, Springer, Berlin, 1972.
Mather, J. N., More Denjoy minimal sets for area preserving diffeomorphisms, Comment. Math. Helvetici 60 (1985), 508–557.
Morrey, C. B., Jr., Multiple integrals in the calculus of variations, Grundlehren # 130, Springer, New York, 1966.
Nabarro, F. R. N., Theory of crystal dislocations, Clarendon Press, Oxford, 1967.
Tonelli, L., Sugli integrali del calcolo delle variazioni in forma ordinaria, Ann. Scuola Norm. Pisa 3 (1934), 401–450 (in L. Tonelli, Opere Scelte vol. III, # 105, Edizioni Cremonese, Roma, 1961).
van der Waals, J. D., The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), verhandel. Konink. Akad. Weten. Amsterdam (Sec. 1) 1 (1893).
von Weizsacker, C. C., Existence of optimal programs of accumulation for an infinite horizon, Rev. Econ. Studies 32 (1965), 85–104.
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Dedicated to Bernard D. Coleman in celebration of his sixtieth birthday
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Leizarowitz, A., Mizel, V.J. One dimensional infinite-horizon variational problems arising in continuum mechanics. Arch. Rational Mech. Anal. 106, 161–194 (1989). https://doi.org/10.1007/BF00251430
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DOI: https://doi.org/10.1007/BF00251430