EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES

doi:10.1016/S0252-9602(15)30091-6

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34K30

Sahbi BOUSSANDEL. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES[J].Acta mathematica scientia,Series B, 2016, 36(1): 233-243.

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[1] Ahmad S. An existence theorem for periodically perturbed conservative systems. Michigan Math J, 1973, 20:385-392
[2] Amann H. On the unique solvability of semi-linear operator equations in Hilbert spaces. J Math Pures Appl, 1982, 61:149-175
[3] Amaral L, Pera M. On periodic solutions of nonconservative systems. Nonlinear Anal, 1982, 6:733-743
[4] Boussandel S. Global existence and maximal regularity of gradient systems. J Differ Equ, 2011, 250(2):929-948
[5] Brown K J. Nonlinear boundary value problems and a global inverse function theorem. Ann Mat Pura Appl, 1975, 106(4):205-217
[6] Brown K J, Lin S S. Periodically perturbed conservative systems and a global inverse functions theorem. Nonlinear Anal, 1980, 4:193-201
[7] Capietto A, Mawhin J, Zanolin F. A continuation approach to superlinear periodic boundary value prob-lems. J Differ Equ, 1990, 88:347-395
[8] Chen Y, Chen J, Wan Z. Remarks on the periodic boundary value problems for first-order differential equations. Comput Math Appl, 1999, 37:49-55
[9] Chen J, O'Regan D. On periodic solutions for even order differential equations. Nonlinear Analysis, 2008, 69:1138-1144
[10] Chill R, Fasangová E. Gradient systems. In:13th International Internet Seminar
[11] Fonda A Sfecci A. A general method for the existence of periodic solutions of differential systems in the plane. J Differ Equ, 2012, 252:1369-1391
[12] Dalmasso R. An existence and uniqueness theorem for a second order nonlinear system. J Math Anal Appl, 2007, 327:715-722
[13] Dalmasso R. Unique solvability for a second order nonlinear system via two global inversion theorems. Ele J Differ Equ, 2008,(11):1-8
[14] Lakshmikantham V, Leela S. Existence and monotone method for periodic solutions of first-oder differential equations. J Math Anal Appl, 1983, 91:237-243
[15] Lin D, Yang Y Zhu D. Periodic solutions for some ordinary differential equations involving stability. Non-linear Analysis, 2001, 45:963-971
[16] Liu Y. Multiple solutions of periodic boundary value problems for first order differential equations. Comput Math Appl, 2007, 54:1-8
[17] Mawhin J. Contractive mappings and periodically perturbed conservative systems. Arch Math, 1976, 12:67-73
[18] Mawhin J. Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS-Regional Conf Math 40. Providence, RI:Amer Math Soc, 1979
[19] Mawhin J. First order ordinary differential equations with several periodic solutions. J Appl Math Phy(ZAMP), 1987, 38:257-265
[20] Mawhin J, Thompson H B. Periodic or bounded solutions of Caretéodory systems of ordinary differential equations. J Dyn Differ Equ, 2003, 15(2/3):327-334
[21] Mawhin J. Topological Fixed Point Theory and Nonlinear Differential Equations. Handbook of Topological Fixed Point Theory. Springer, 2005
[22] Nagle R K, Sinkala Z. Existence of 2π-periodic solutions for nonlinear systems of first-order ordinary differential equations at resonance. Nonlinear Analysis, TMA, 1995, 25:l-16
[23] Nieto J J, Alvarez-Noriega N. Periodic boundary value problems for nonlinear first order ordinary differential equations. Acta Math Hungar, 1996, 71(1/2):49-58
[24] Plastock R. Homeomorphisms between Banach spaces. Trans Amer Math Soc, 1974, 200:169-183
[25] Rabier P J, Stuart C A. Boundary value problems for first order systems on the half-line. Topol Methods Nonlinear Anal, 2005, 25(1):101-133
[26] Radulescu M, Radulescu S. Global inversion theorems and applications to differential equations. Nonlinear Analysis, TMA, 1980, 4(4):951-965
[27] Radulescu M, Radulescu S. An application of Hadamard-Levy theorem to a scalar initial value problem. Proc Amer Math Soc, 1989, 106(1):139-143
[28] Radulescu M, Radulescu S. An application of a global inversion theorem to a Dirichlet problem for a second order differential equation. Rev Roumaine Math Pures Appl, 1992, 37:929-933
[29] Radulescu M, Radulescu S. Applications of a global inversion theorem to unique solvability of second order Dirichlet problems. An Univ Craiova, Math Comp Sci Ser, 2003, 30(1):198-203
[30] Radulescu M, Radulescu S. Global inversion theorems and applications to unique solvability of boundary value theorems for differential equations. Int J Differ Equ Appl, 2000, 1(2):159-166
[31] Rynne B P, Youngson M A. Linear Functional Analysis. Springer Undergraduate Mathematics Series. Springer, 2008
[32] Tisdell C C. Existence of solutions to first-order periodic boundary value problems. J Math Anal Appl, 2006, 323:1325-1332
[33] Trif T. Unique solvability of certain nonlinear boundary value problems via a global inversion theorem of Hadamard-Levy type. Demonstratio Math, 2005, 38(2):331-340
[34] Vidossich G. Multiple periodic solutions for first-order ordinary differential equations. J Math Anal Appl, 1987, 127:459-469
[35] Li W G. An application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations. Nonlinear Analysis, 2009, 70:3730-3737
[36] Yang X. Existence and uniqueness results for periodic solution of nonlinear differential equations. Appl Math Comput, 2002, 130:213-223

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES

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