Almost periodic solutions of second-order systems with monotone fields on a compact subset

Nonlinear Analysis, Theory, Methods and Applications

Volumn 53, Issue 6, 2003, Pages 751-763

  Cieutat, Philippe ^a  

^a UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

Author keywords

Almost periodic solutions; Bounded solutions; Second order differential equations

Indexed keywords

COMPUTATIONAL METHODS; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

COMPACT SUBSETS;

DIFFERENTIAL EQUATIONS;

EID: 0037409382     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00026-9     Document Type: Article

References (13)

1. Berger M.S., Chen Y.Y. Forced quasiperiodic and almost periodic solution for nonlinear systems. Nonlinear Anal. TMA. 21:1993;949-965.
2. Berger M.S., Zhang L. New method for large quasiperiodic nonlinear oscillations with fixed frequencies for the nondissipative second type Duffing equation. Topological Methods Nonlinear Anal. 6:1995;283-293.
3. Berger M.S., Zhang L. A new method for large quasiperiodic nonlinear oscillations with fixed frequencies for the nondissipative conservative systems. Commun. Appl. Nonlinear Anal. 2:1995;79-106.
4. Blot J., Cieutat P., Mawhin J. Almost-periodic oscillations of monotone second-order systems. Adv. in Differential Equations. 2:1997;693-714.
5. Carminati C. Forced systems with almost periodic and quasiperiodic forcing term. Nonlinear Anal. TMA. 32:1998;727-739.
6. Corduneanu C. Almost Periodic Functions. 1968;Wiley, New York. Reprinted, Chelsea, New York, 1989.
7. Fink A.M. Almost Periodic Differential Equations. Lecture Notes in Mathematics. Vol. 377:1974;Springer, Berlin.
8. J.B. Hiriart-Urruty, C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. I, Springer, Berlin, 1993.
9. Krasnosel'skii M.A. The Operator of Translation Along Trajectories of Differential Equations. Transl. Math. Monographs. Vol. 19:1968;Amer. Math. Soc. Providence, RI.
10. J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conference No. 40, Amer. Math. Soc., Providence, RI, 1979.
11. J. Mawhin, Bounded and almost periodic solutions of nonlinear differential equations: variational vs nonvariational approach, in: Calculus of Variations and Differential Equations (Haifa, 1998), Chapman & Hall/CRC Research Notes in Mathematics, Vol. 410, Chapman & Hall/CRC, Boca Raton, Raton, FL, 2000, pp. 167-184.
12. Yoshizawa T. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. 1975;Springer, New York.
13. Zakharin S.F., Parasyuk I.O. Generalized and classical almost periodic solutions of Lagrangian systems. Funkcial. Ekvac. 42:1999;325-338.