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Clarke duality for Hamiltonian systems with nonstandard growth

Abstract

We consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS no. 188, pages 1 - 21,
ISSN: 0362-546X
Language:
English
Publication year:
2019
Bibliographic description:
Acinas S., Maksymiuk J., Mazzone F.: Clarke duality for Hamiltonian systems with nonstandard growth// NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. -Vol. 188, (2019), s.1-21
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.na.2019.05.017
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  1. J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems, Springer-Verlag, New York, 1989. open in new tab
  2. Y. Tian, W. Ge, Periodic solutions of non-autonomous second-order sys- tems with a p-Laplacian, Nonl. Anal. TMA 66 (1) (2007) 192-203. open in new tab
  3. F. H. Clarke, A classical variational principle for periodic Hamiltonian tra- jectories, Proc. Am. Math. Soc. 76. open in new tab
  4. F. H. Clarke, Periodic solutions to Hamiltonian inclusions, J. Diff. Eq. 40. open in new tab
  5. F. H. Clarke, I. Ekeland, Nonlinear oscillations and boundary value prob- lems for Hamiltonian systems, Arch. Rat. Mech. Math. 78. open in new tab
  6. I. Ekeland, Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, J. Diff. Eq 34. open in new tab
  7. I. Ekeland, Convexity Methods in Hamiltonian Mechanics, 1st Edition, Springer-Verlag Berlin Heidelberg, 1990. open in new tab
  8. F. H. Clarke, I. Ekeland, Hamiltonian trajectories having prescribed mini- mal period, Comm. Pure Appl. Math. 33. open in new tab
  9. J.-B. Hiriart-Urruty, C. Lemaréchal, Fundamentals of convex analysis, Springer Science & Business Media, 2001. open in new tab
  10. S. Acinas, F. Mazzone, Periodic solutions of Euler-Lagrange equations in an anisotropic Orlicz-Sobolev space setting, Revista de la Unión Matemática Argentina (In press).
  11. G. Barletta, A. Cianchi, Dirichlet problems for fully anisotropic elliptic equations, Proc. Royal Soc. Edinburgh 147 (1) (2017) 25-60. open in new tab
  12. M. Chmara, J. Maksymiuk, Anisotropic Orlicz-Sobolev spaces of vector valued functions and Lagrange equations, J. Math. Anal. Appl. 456 (1) (2017) 457-475. open in new tab
  13. G. Schappacher, A notion of Orlicz spaces for vector valued functions, Appl. Math. 50 (4) (2005) 355-386. open in new tab
  14. N. Trudinger, An imbedding theorem for H 0 (G, Ω)-spaces, Studia Math. 50 (1) (1974) 17-30. open in new tab
  15. A. Fiorenza, M. Krbec, Indices of Orlicz spaces and some applications, Comment. Math. Univ. Carolin. 38 (3) (1997) 433-451.
  16. M. Chmara, J. Maksymiuk, Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space, J. Math. Anal. Appl. 470 (1) (2019) 584-598. open in new tab
  17. M. A. Krasnosielskiȋ, J. B. Rutickiȋ, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961.
  18. S. Acinas, G. Giubergia, F. Mazzone, E. Schwindt, On estimates for the period of solutions of equations involving the φ-Laplace operator, J. Abstr. Differ. Equ. Appl. 5 (1) (2014) 21-34. open in new tab
  19. R. Manásevich, J. Mawhin, The spectrum of p-Laplacian systems under Dirichlet, Neumann and periodic boundary conditions, Morse theory, min- imax theory and their applications to nonlinear differential equations (1999) 201-216. open in new tab
  20. L. Maligranda, Orlicz spaces and interpolation, Vol. 5 of Seminários de Matemática [Seminars in Mathematics], Universidade Estadual de Camp- inas, Departamento de Matemática, Campinas, 1989.
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