Constrained variational problems governed by second-order Lagrangians

References

• Dirac PAM, Fock VA, Podolski B. On quantum electrodynamics. Phys Z der Sowjetunion. 1932;2(6):468–479.
   Google Scholar
• Tomonaga S. On a relativistically invariant formulation of the quantum theory of wave fields. Prog Theor Phys. 1946;1(2):27–42. doi: 10.1143/PTP.1.27
   Google Scholar
• Petrat S, Tumulka R. Multi-time wave functions for quantum field theory. Ann Phys. 2014;345:17–54. doi: 10.1016/j.aop.2014.03.004
   Web of Science ®Google Scholar
• Lienert M, Nickel L. A simple explicitly solvable interacting relativistic N-particle model. J Phys A: Math Theor. 2015;48:325301.
   Web of Science ®Google Scholar
• Deckert DA, Nickel L. Consistency of multi-time Dirac equations with general interaction potentials. J Math Phys. 2016;57:072301. doi: 10.1063/1.4954947
   Web of Science ®Google Scholar
• Keppeler S, Sieber M. Particle creation and annihilation at interior boundaries: one-dimensional models, arXiv:1511.03071
   Google Scholar
• Teufel S, Tumulka R. New type of Hamiltonians without ultraviolet divergence for quantum field theories, arXiv:1505.04847v1
   Google Scholar
• Friedman A. The Cauchy problem in several time variables. J Math Mech. 1962;11(6):859–889.
   Google Scholar
• Yurchuk NI. A partially characteristic mixed boundary value problem with Goursat initial conditions for linear equations with two-dimensional time. Differ Equations. 1969;5:898–910.
   Google Scholar
• Kendall WS. Contours of Brownian processes with several-dimensional times. Probab Theory Relat Fields. 1980;52(3):267–276.
   Google Scholar
• Rochet JC. The taxation principle and multitime Hamilton-Jacobi equations. J Math Econom. 1985;14(2):113–128. doi: 10.1016/0304-4068(85)90015-1
   Web of Science ®Google Scholar
• Saunders DJ. The Geometry of Jet Bundles. Cambridge: Cambridge University Press; 1989. (London Math. Soc. Lecture Notes Series; vol. 142).
   Google Scholar
• Bouziani A. On the solvability of nonlocal pluriparabolic problems. Electron J Differ Equ. 2001;2001(21):1–16.
   Google Scholar
• Khoshnevisan D, Xiao Y, Zhong Y. Local times of additive Levy processe. Stoch Process Their Appl. 2003;104(2):193–216. doi: 10.1016/S0304-4149(02)00237-5
   Web of Science ®Google Scholar
• Motta M, Rampazzo F. Nonsmooth multi-time Hamilton-Jacobi systems. Indiana Univ Math J. 2006;55(5):1573–1614. doi: 10.1512/iumj.2006.55.2760
   Web of Science ®Google Scholar
• Udrişte C, Ţevy I. Multi-time Euler-Lagrange-Hamilton theory. WSEAS Trans Math. 2007;6(6):701–709.
   Google Scholar
• Udrişte C, Matei L. Lagrange-Hamilton theories. Bucharest: Geometry Balkan Press; 2008. (Monographs and Textbooks; vol. 8). Romanian
   Google Scholar
• Cardin F, Viterbo C. Commuting Hamiltonians and Hamilton-Jacobi multi-time equations. Duke Math J. 2008;144(2):235–284. doi: 10.1215/00127094-2008-036
   Web of Science ®Google Scholar
• Prepeliţă V. Minimal realization algorithm for multidimensional hybrid systems. WSEAS Trans. Sys. 2009;8(1):22–33.
   Google Scholar
• Benrabah A, Rebbani F, Boussetila N. A study of the multitime evolution equation with time-nonlocal conditions. Balkan J Geom Appl. 2011;16(2):13–24.
   Google Scholar
• Damian V. Multitime stochastic optimal control [PhD thesis]. Bucharest: University “Politehnica” of Bucharest; 2011
   Google Scholar
• Ghiu C. Controllability of multitime linear PDEs systems [PhD thesis]. Bucharest: University “Politehnica” of Bucharest; 2013
   Google Scholar
• Treanţă S. PDEs of Hamilton-Pfaff type via multi-time optimization problems. UPB Sci Bull, Series A: Appl Math Phys. 2014;76(1):163–168.
   Google Scholar
• Treanţă S. On multi-time Hamilton-Jacobi theory via second order Lagrangians. UPB Sci Bull, Series A: Appl Math Phys. 2014;76(3):129–140.
   Google Scholar
• Treanţă S. Multiobjective fractional variational problem on higher-order jet bundles. Commun Math Stat. 2016;4(3):323–340. doi: 10.1007/s40304-016-0087-0
   Web of Science ®Google Scholar
• Treanţă S. Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE. Comput Math Appl. 2018;75(2):547–560. doi: 10.1016/j.camwa.2017.09.033
   Web of Science ®Google Scholar
• Treanţă S. Efficiency in generalized V-KT-pseudoinvex control problems. Int J Control. 2018; DOI:10.1080/00207179.2018.1483082.
   Web of Science ®Google Scholar
• Mititelu Şt., Treanţă S. Efficiency conditions in vector control problems governed by multiple integrals. J Appl Math Comput. 2018;57(1–2):647–665. doi: 10.1007/s12190-017-1126-z
   Web of Science ®Google Scholar
• Miron R. The geometry of higher order Lagrange spaces. Applications to mechanics and physics. FTPH no. 82. Dordrecht: Kluwer; 1997
   Google Scholar
• Krupka D. On the higher order Hamilton theory in fibered spaces. Geometrical methods in physics, proceedings of the conference on differential geometry and its applications, Nove Mesto na Morave, Czechoslovakia; 1983 Sep 5–9; J.E. Purkyne Univ., Brno; 1984. p. 167–184
   Google Scholar
• Treanţă S. Hamilton-Jacobi system of PDEs governed by higher-order Lagrangians. Trans J Math Anal Appl. 2017;5(1):1–15.
   Google Scholar
• Treanţă S. Gauge Transformation Moments and Generating Functions for Higher-Order Lagrangians. Res Commun Math Math Sci. 2017;8(1):1–16.
   Google Scholar