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Existence of nonstationary periodic solutions for $\Gamma$-symmetric Lotka-Volterra type systems
Well-posedness of initial value problems for functional differential and algebraic equations of mixed type
1. | Division of Applied Mathematics - Brown University, 182 George Street, Providence, RI 02912, United States |
2. | Laboratory of Mathematics, Images and Applications - University of La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle, France |
References:
[1] |
M. Bambi, Endogenous growth and time-to-build: the AK case, J. Economic Dynamics and Control, 32 (2008), 1015-1040.
doi: 10.1016/j.jedc.2007.04.002. |
[2] |
R. Boucekkine, O. Licandro, L. A. Puch and F. D. Rio, Vintage capital and the dynamics of the AK model, J. Economic Theory, 120 (2005), 39-72.
doi: 10.1016/j.jet.2004.02.006. |
[3] |
D. Cass and M. E. Yaari, Individual saving, aggregate capital accumulation and efficient growth, in "Essays on the Theory of Optimal Growth," K. Shell (ed.), MIT Press, Cambridge, MA, (1967), 233-268. |
[4] | |
[5] |
H. d'Albis and E. Augeraud-Véron, Competitive growth in a life-cycle model: Existence and dynamics, International Economic Review, 50 (2009), 459-484.
doi: 10.1111/j.1468-2354.2009.00537.x. |
[6] |
P. A. Diamond, National debt in a neoclassical growth model, American Economic Review, 55 (1965), 1126-1150. |
[7] |
O. Diekmann, S. A. van Gils, S. M. Verduyn-Lunel and H. O. Walther, "Delay Equations," Springer-Verlag, New York, 1995. |
[8] |
C. Edmond, An integral equation representation for overlapping generations in continuous time, J. Economic Theory, 143 (2008), 596-609.
doi: 10.1016/j.jet.2008.03.006. |
[9] |
D. Gale, Pure exchange equilibrium of dynamic economic models, J. Economic Theory, 6 (1973), 12-36.
doi: 10.1016/0022-0531(73)90041-0. |
[10] |
J. D. Geanakoplos and H. M. Polemarchakis, Walrasian indeterminacy and keynesian macroeconomics, Rev. Economic Studies, 53 (1986), 755-779.
doi: 10.2307/2297718. |
[11] |
J. Grandmont, On endogenous competitive business cycles, Econometrica, 53 (1985), 995-1045.
doi: 10.2307/1911010. |
[12] |
J. K. Hale and S. M. Verduyn-Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York, 1993. |
[13] |
J. Härterich, B. Sandstede and A. Scheel, Exponential dichotomies for linear non-autonomous functional differential equations of mixed type, Indiana Univ. Math. J., 51 (2002), 1081-1109.
doi: 10.1512/iumj.2002.51.2188. |
[14] |
D. K. Hughes, Variational and optimal control problems with delayed argument, J. Optimization Theory Appl., 2 (1968), 1-14.
doi: 10.1007/BF00927159. |
[15] |
H. J. Hupkes, E. Augeraud-Veron and S. M. Verduyn-Lunel, Center projections for smooth difference equations of mixed type, J. Diff. Eqn., 244 (2008), 803-835.
doi: 10.1016/j.jde.2007.10.033. |
[16] |
H. J. Hupkes and S. M. Verduyn-Lunel, Center manifold theory for functional differential equations of mixed type, J. Dyn. Diff. Eq., 19 (2007), 497-560.
doi: 10.1007/s10884-006-9055-9. |
[17] |
H. J. Hupkes and S. M. Verduyn-Lunel, Lin's method and homoclinic bifurcations for functional differential equations of mixed type, Indiana Univ. Math. J., 58 (2009), 2433-2487.
doi: 10.1512/iumj.2009.58.3661. |
[18] |
F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370.
doi: 10.2307/1913386. |
[19] |
B. J. Levin, "Distribution of Zeros of Entire Functions (translated from Russian)," American Mathematical Society, Providence, 1980. |
[20] |
T. Lloyd-Braga, C. Nourry and A. Venditti, Indeterminacy in dynamic models: when Diamond meets Ramsey, J. Economic Theory, 134 (2007), 513-536.
doi: 10.1016/j.jet.2005.12.005. |
[21] |
J. Mallet-Paret, The fredholm alternative for functional differential equations of mixed type, J. Dyn. Diff. Eq., 11 (1999), 1-48.
doi: 10.1023/A:1021889401235. |
[22] |
J. Mallet-Paret and S. M. Verduyn-Lunel, Exponential dichotomies and Wiener-Hopf factorizations for mixed-type functional differential equations,, J. Diff. Eq., ().
|
[23] |
P. M. Romer, Increasing returns and long-run growth, J. Political Economy, 94 (1986), 1002-1037.
doi: 10.1086/261420. |
[24] |
A. Rustichini, Functional differential equations of mixed type: the linear autonomous case, J. Dyn. Diff. Eq., 11 (1989), 121-143.
doi: 10.1007/BF01047828. |
[25] |
A. Rustichini, Hopf bifurcation for functional-differential equations of mixed type, J. Dyn. Diff. Eq., 11 (1989), 145-177.
doi: 10.1007/BF01047829. |
[26] |
P. A. Samuelson, An exact consumption-loan model of interest with or without the social contrivance of money, J. Political Economy, 66 (1958), 467-482.
doi: 10.1086/258100. |
[27] |
J. Tirole, Asset bubbles and overlapping generations, Econometrica, 53 (1985), 1071-1100.
doi: i:10.2307/1911012. |
[28] |
A. Venditti and K. Nishimura, Indeterminacy in discrete-time infinite-horizon models, in "Handbook of Optimal Growth: Vol. 1: The Discrete Time Horizon," R.A. Dana, C. Le Van, T. Mitra and K. Nishimura (eds.), Kluwer, (2006), 273-296. |
show all references
References:
[1] |
M. Bambi, Endogenous growth and time-to-build: the AK case, J. Economic Dynamics and Control, 32 (2008), 1015-1040.
doi: 10.1016/j.jedc.2007.04.002. |
[2] |
R. Boucekkine, O. Licandro, L. A. Puch and F. D. Rio, Vintage capital and the dynamics of the AK model, J. Economic Theory, 120 (2005), 39-72.
doi: 10.1016/j.jet.2004.02.006. |
[3] |
D. Cass and M. E. Yaari, Individual saving, aggregate capital accumulation and efficient growth, in "Essays on the Theory of Optimal Growth," K. Shell (ed.), MIT Press, Cambridge, MA, (1967), 233-268. |
[4] | |
[5] |
H. d'Albis and E. Augeraud-Véron, Competitive growth in a life-cycle model: Existence and dynamics, International Economic Review, 50 (2009), 459-484.
doi: 10.1111/j.1468-2354.2009.00537.x. |
[6] |
P. A. Diamond, National debt in a neoclassical growth model, American Economic Review, 55 (1965), 1126-1150. |
[7] |
O. Diekmann, S. A. van Gils, S. M. Verduyn-Lunel and H. O. Walther, "Delay Equations," Springer-Verlag, New York, 1995. |
[8] |
C. Edmond, An integral equation representation for overlapping generations in continuous time, J. Economic Theory, 143 (2008), 596-609.
doi: 10.1016/j.jet.2008.03.006. |
[9] |
D. Gale, Pure exchange equilibrium of dynamic economic models, J. Economic Theory, 6 (1973), 12-36.
doi: 10.1016/0022-0531(73)90041-0. |
[10] |
J. D. Geanakoplos and H. M. Polemarchakis, Walrasian indeterminacy and keynesian macroeconomics, Rev. Economic Studies, 53 (1986), 755-779.
doi: 10.2307/2297718. |
[11] |
J. Grandmont, On endogenous competitive business cycles, Econometrica, 53 (1985), 995-1045.
doi: 10.2307/1911010. |
[12] |
J. K. Hale and S. M. Verduyn-Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York, 1993. |
[13] |
J. Härterich, B. Sandstede and A. Scheel, Exponential dichotomies for linear non-autonomous functional differential equations of mixed type, Indiana Univ. Math. J., 51 (2002), 1081-1109.
doi: 10.1512/iumj.2002.51.2188. |
[14] |
D. K. Hughes, Variational and optimal control problems with delayed argument, J. Optimization Theory Appl., 2 (1968), 1-14.
doi: 10.1007/BF00927159. |
[15] |
H. J. Hupkes, E. Augeraud-Veron and S. M. Verduyn-Lunel, Center projections for smooth difference equations of mixed type, J. Diff. Eqn., 244 (2008), 803-835.
doi: 10.1016/j.jde.2007.10.033. |
[16] |
H. J. Hupkes and S. M. Verduyn-Lunel, Center manifold theory for functional differential equations of mixed type, J. Dyn. Diff. Eq., 19 (2007), 497-560.
doi: 10.1007/s10884-006-9055-9. |
[17] |
H. J. Hupkes and S. M. Verduyn-Lunel, Lin's method and homoclinic bifurcations for functional differential equations of mixed type, Indiana Univ. Math. J., 58 (2009), 2433-2487.
doi: 10.1512/iumj.2009.58.3661. |
[18] |
F. E. Kydland and E. C. Prescott, Time to build and aggregate fluctuations, Econometrica, 50 (1982), 1345-1370.
doi: 10.2307/1913386. |
[19] |
B. J. Levin, "Distribution of Zeros of Entire Functions (translated from Russian)," American Mathematical Society, Providence, 1980. |
[20] |
T. Lloyd-Braga, C. Nourry and A. Venditti, Indeterminacy in dynamic models: when Diamond meets Ramsey, J. Economic Theory, 134 (2007), 513-536.
doi: 10.1016/j.jet.2005.12.005. |
[21] |
J. Mallet-Paret, The fredholm alternative for functional differential equations of mixed type, J. Dyn. Diff. Eq., 11 (1999), 1-48.
doi: 10.1023/A:1021889401235. |
[22] |
J. Mallet-Paret and S. M. Verduyn-Lunel, Exponential dichotomies and Wiener-Hopf factorizations for mixed-type functional differential equations,, J. Diff. Eq., ().
|
[23] |
P. M. Romer, Increasing returns and long-run growth, J. Political Economy, 94 (1986), 1002-1037.
doi: 10.1086/261420. |
[24] |
A. Rustichini, Functional differential equations of mixed type: the linear autonomous case, J. Dyn. Diff. Eq., 11 (1989), 121-143.
doi: 10.1007/BF01047828. |
[25] |
A. Rustichini, Hopf bifurcation for functional-differential equations of mixed type, J. Dyn. Diff. Eq., 11 (1989), 145-177.
doi: 10.1007/BF01047829. |
[26] |
P. A. Samuelson, An exact consumption-loan model of interest with or without the social contrivance of money, J. Political Economy, 66 (1958), 467-482.
doi: 10.1086/258100. |
[27] |
J. Tirole, Asset bubbles and overlapping generations, Econometrica, 53 (1985), 1071-1100.
doi: i:10.2307/1911012. |
[28] |
A. Venditti and K. Nishimura, Indeterminacy in discrete-time infinite-horizon models, in "Handbook of Optimal Growth: Vol. 1: The Discrete Time Horizon," R.A. Dana, C. Le Van, T. Mitra and K. Nishimura (eds.), Kluwer, (2006), 273-296. |
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