Title | PERIODIC SOLUTIONS OF LAGRANGIAN SYSTEMS OF RELATIVISTIC OSCILLATORS |
Publication Type | Journal Article |
Year of Publication | 2011 |
Authors | BREZIS, HAIM, MAWHIN, JEAN |
Secondary Title | Communications in Applied Analysis |
Volume | 15 |
Issue | 2 |
Start Page | 235 |
Pagination | 250 |
Date Published | 04/2011 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 34C25; 47H11; 49J40; 58E30; 58E35;78A35. |
Abstract | T-periodic solutions of systems of differential equations of the form
where φ = ∇Φ, with Φ strictly convex, is a homeomorphism of the ball onto , are considered under various conditions upon F and h. The approach is mostly variational, but requires the use of results on an auxiliary system based upon fixed point theory and Leray-Schauder degree.
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URL | http://www.acadsol.eu/en/articles/15/2/8.pdf |
Short Title | PERIODIC SOLUTIONS OF LAGRANGIAN SYSTEMS OF RELATIVISTIC OSCILLATORS |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] S. Ahmad, A.C. Lazer, J.L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems, Indiana Univ. Math. J. 25 (1976), 933–944.
[2] C. Bereanu, J. Mawhin, Existence and multiplicity results for some nonlinear problems with singular φ-laplacian, J. Differential Equations 243 (2007), 536–557. [3] C. Bereanu, J. Mawhin, Boundary value problems for some nonlinear systems with singular φ-Laplacian, J. Fixed Point Theory Appl. 4 (2008), 57–75. [4] M.S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York, 1977. [5] M.S. Berger, M. Schechter, On the solvability of semi-linear gradient operator equations, Adv. in Math. 25 (1977), 97–132. [6] H. Brezis, J. Mawhin, Periodic solutions of the forced relativistic pendulum, Differential Integral Equations 23 (2010), 801–810. [7] K.C. Chang, On the periodic nonlinearity and the multiplicity of solutions, Nonlinear Anal. 13 (1989), 527–537. [8] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985. [9] J. Ma, C.L. Tang, Periodic solutions for some nonautonomous second-order systems, J. Math. Anal. Appl. 275 (2002), 482–494. [10] J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Series No. 40, American Math. Soc., Providence, 1979. [11] J. Mawhin, Forced second order conservative systems with periodic nonlinearity, Ann. Inst. Henri-Poincar ́e Anal. Non Lin ́eaire 6 suppl. (1989), 415–434. [12] J. Mawhin, Periodic solutions of the forced pendulum: classical vs relativistic, Le Matematiche 65 (2010), 97–107. [13] J. Mawhin, M. Willem, Variational methods and boundary value problems for vector second order differential equations and applications to the pendulum equation, in: Nonlinear Analysis and Optimization, Lect. Notes Math. No. 1107, Springer, Berlin, 1984, 181–192.
[14] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. [15] P. Rabinowitz, On a class of functionals invariant under a Z n action, Trans. Amer. Math. Soc. 310 (1988), 303–311. [16] M. Schechter, Periodic non-autonomous second-order dynamical systems, J. Differential Equations 223 (2006), 290–302. [17] C.L. Tang, Periodic solutions of non-autonomous second order systems with γ-quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), 671–675. [18] C.L. Tang, Periodic solutions of non-autonomous second order systems, J. Math. Anal. Appl. 202 (1996), 465–469. [19] C.L. Tang, Some existence results for periodic solutions of non-autonomous second order systems. Acad. Roy. Belg. Bull. Cl. Sci. (6) 8 (1997),13–19. [20] C.L. Tang, Periodic solutions for nonautonomous second order systems with sublinear nonlinearity. Proc. Amer. Math. Soc. 126 (1998), 3263–3270. [21] C.L. Tang, X.P. Wu, Periodic solutions for second order systems with not uniformly coercive potential, J. Math. Anal. Appl. 259 (2001), 386–397. [22] C.L. Tang, X.P. Wu, Notes on periodic solutions of subquadratic second order systems, J. Math. Anal. Appl. 285 (2003), 8–16. [23] C.L. Tang, X.P. Wu, A note on periodic solutions of nonautonomous second-order systems, Proc. Amer. Math. Soc. 132 (2004), 1295–1303. [24] Y. Tian, G.S. Zhang, W.G. Ge, Periodic solutions for a quasilinear non-autonomous second-order system, J. Appl. Math. Comput. 22 (2006), 263–271. [25] Z.Y. Wang, J.H. Zhang, Periodic solutions of non-autonomous second order systems with p-Laplacian, Electronic J. Differential Equations 2009-17 (2009), 1–12. [26] X.P. Wu, Periodic solutions for nonautonomous second-order systems with bounded nonlinearity, J. Math. Anal. Appl. 230 (1999), 135–141. [27] X.P. Wu, C.L. Tang, Periodic solutions of a class of nonautonomous second order systems, J. Math. Anal. Appl. 236 (1999), 227–235. [28] F.K. Zhao, X. Wu, Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity, Nonlinear Anal. 60 (2005), 325–335. |