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From Frank Ramsey to René Thom: A classical problem in the calculus of variations leading to an implicit differential equation
1.  Canada Research Chair in Mathematical Economics, Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada 
[1] 
Renato Iturriaga, Héctor SánchezMorgado. Limit of the infinite horizon discounted HamiltonJacobi equation. Discrete & Continuous Dynamical Systems  B, 2011, 15 (3) : 623635. doi: 10.3934/dcdsb.2011.15.623 
[2] 
Agnieszka B. Malinowska, Delfim F. M. Torres. EulerLagrange equations for composition functionals in calculus of variations on time scales. Discrete & Continuous Dynamical Systems  A, 2011, 29 (2) : 577593. doi: 10.3934/dcds.2011.29.577 
[3] 
Senda Ounaies, JeanMarc Bonnisseau, Souhail Chebbi, Halil Mete Soner. Merton problem in an infinite horizon and a discrete time with frictions. Journal of Industrial & Management Optimization, 2016, 12 (4) : 13231331. doi: 10.3934/jimo.2016.12.1323 
[4] 
Tao Pang, Azmat Hussain. An infinite time horizon portfolio optimization model with delays. Mathematical Control & Related Fields, 2016, 6 (4) : 629651. doi: 10.3934/mcrf.2016018 
[5] 
Sebastián Ferrer, Martin Lara. Families of canonical transformations by HamiltonJacobiPoincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223241. doi: 10.3934/jgm.2010.2.223 
[6] 
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and HamiltonJacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159198. doi: 10.3934/jgm.2010.2.159 
[7] 
Bernard Dacorogna, Giovanni Pisante, Ana Margarida Ribeiro. On non quasiconvex problems of the calculus of variations. Discrete & Continuous Dynamical Systems  A, 2005, 13 (4) : 961983. doi: 10.3934/dcds.2005.13.961 
[8] 
Daniel Faraco, Jan Kristensen. Compactness versus regularity in the calculus of variations. Discrete & Continuous Dynamical Systems  B, 2012, 17 (2) : 473485. doi: 10.3934/dcdsb.2012.17.473 
[9] 
Monika Dryl, Delfim F. M. Torres. Necessary optimality conditions for infinite horizon variational problems on time scales. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 145160. doi: 10.3934/naco.2013.3.145 
[10] 
Felix Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Conference Publications, 2003, 2003 (Special) : 760770. doi: 10.3934/proc.2003.2003.760 
[11] 
Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 38213838. doi: 10.3934/dcdsb.2017192 
[12] 
Xiaoshan Chen, Xun Li, Fahuai Yi. Optimal stopping investment with nonsmooth utility over an infinite time horizon. Journal of Industrial & Management Optimization, 2019, 15 (1) : 8196. doi: 10.3934/jimo.2018033 
[13] 
Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 17431767. doi: 10.3934/dcdsb.2018235 
[14] 
Delfim F. M. Torres. Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 491500. doi: 10.3934/cpaa.2004.3.491 
[15] 
Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete & Continuous Dynamical Systems  A, 2011, 29 (2) : 417437. doi: 10.3934/dcds.2011.29.417 
[16] 
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449461. doi: 10.3934/eect.2016013 
[17] 
Nikos Katzourakis. Nonuniqueness in vectorvalued calculus of variations in $L^\infty$ and some Linear elliptic systems. Communications on Pure & Applied Analysis, 2015, 14 (1) : 313327. doi: 10.3934/cpaa.2015.14.313 
[18] 
Gisella Croce, Nikos Katzourakis, Giovanni Pisante. $\mathcal{D}$solutions to the system of vectorial Calculus of Variations in $L^∞$ via the singular value problem. Discrete & Continuous Dynamical Systems  A, 2017, 37 (12) : 61656181. doi: 10.3934/dcds.2017266 
[19] 
Ioan Bucataru, Matias F. Dahl. Semibasic 1forms and Helmholtz conditions for the inverse problem of the calculus of variations. Journal of Geometric Mechanics, 2009, 1 (2) : 159180. doi: 10.3934/jgm.2009.1.159 
[20] 
Hans Josef Pesch. Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 161173. doi: 10.3934/naco.2013.3.161 
2017 Impact Factor: 1.179
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