Free Access
Volume 19, Number 2, April-June 2013
Page(s) 404 - 437
Published online 23 January 2013
  1. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston (1997). [Google Scholar]
  2. M. Bardi and F. Da Lio, On the Bellman equation for some unbounded control problems. NoDEA 4 (1997) 491–510. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Barles, Existence results for first order Hamilton-Jacobi equations. Ann. Inst. Henri Poincaré 1 (1984) 325–340. [Google Scholar]
  4. S. Biton, Nonlinear monotone semigroups and viscosity solutions. Ann. Inst. Henri Poincaré 18 (2001) 383–402. [CrossRef] [Google Scholar]
  5. M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 277 (1983) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  6. M.G. Crandall and P.L. Lions, On existence and uniqueness of solutions of Hamilton-Jacobi equations. Nonlinear Anal. 10 (1986) 353–370. [CrossRef] [MathSciNet] [Google Scholar]
  7. M.G. Crandall and P.L. Lions, Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Ill. J. Math. 31 (1987) 665–688. [Google Scholar]
  8. F. Da Lio, On the Bellman equation for infinite horizon problems with unblounded cost functional. Appl. Math. Optim. 41 (2000) 171–197. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Da Lio and O. Ley, Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications. SIAM J. Control Optim. 45 (2006) 74–106. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Da Lio and O. Ley, Convex Hamilton-Jacobi equations under superlinear growth conditions on data. Appl. Math. Optim. 63 (2011) 309–339. [CrossRef] [MathSciNet] [Google Scholar]
  11. R.J. Elliott and N.J. Kalton, The existence of value in differential games. Amer. Math. Soc., Providence, RI. Memoirs of AMS 126 (1972). [Google Scholar]
  12. L.C. Evans and P.E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations. Indiana Univ. Math. J. 5 (1984) 773–797. [CrossRef] [MathSciNet] [Google Scholar]
  13. W.H. Fleming and P.E. Souganidis, On the existence of value functions of two-players, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989) 293–314. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Friedman and P.E. Souganidis, Blow-up solutions of Hamilton-Jacobi equations. Commun. Partial Differ. Equ. 11 (1986) 397–443. [CrossRef] [Google Scholar]
  15. M. Garavello and P. Soravia, Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost. NoDEA 11 (2004) 271–298. [CrossRef] [MathSciNet] [Google Scholar]
  16. H. Ishii, Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Indiana Univ. Math. J. 33 (1984) 721–748. [CrossRef] [MathSciNet] [Google Scholar]
  17. H. Ishii, Representation of solutions of Hamilton-Jacobi equations. Nonlinear Anal. 12 (1988) 121–146. [CrossRef] [MathSciNet] [Google Scholar]
  18. P.L. Lions, Generalized Solutions of Hamilton-Jacobi equations. Pitman, London (1982). [Google Scholar]
  19. P.L. Lions and P.E. Souganidis, Differential games, optimal conrol and directional derivatives of viscosity solutions of Bellman’s and Isaacs’ equations. SIAM J. Control Optim. 23 (1985) 566–583. [CrossRef] [MathSciNet] [Google Scholar]
  20. W. McEneaney, A uniqueness result for the Isaacs equation corresponding to nonlinear H control. Math. Control Signals Syst. 11 (1998) 303–334. [CrossRef] [Google Scholar]
  21. F. Rampazzo, Differential games with unbounded versus bounded controls. SIAM J. Control Optim. 36 (1998) 814–839. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Soravia, Equivalence between nonlinear ℋ control problems and existence of viscosity solutions of Hamilton-Jacobi-Isaacs equations. Appl. Math. Optim. 39 (1999) 17–32. [CrossRef] [MathSciNet] [Google Scholar]
  23. P.E. Souganidis, Existence of viscosity solution of Hamilton-Jacobi equations. J. Differ. Equ. 56 (1985) 345–390. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Yong, Zero-sum differential games involving impusle controls. Appl. Math. Optim. 29 (1994) 243–261. [CrossRef] [MathSciNet] [Google Scholar]
  25. Y. You, Syntheses of differential games and pseudo-Riccati equations. Abstr. Appl. Anal. 7 (2002) 61–83. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.