Periodic solutions for noncoercive superquadratic Hamiltonian systems

• Autorzy: Timoumi M.
• Języki publikacji: EN

Abstrakty

EN

In this note, we study the existence of periodic solutions for the noncoer- cive Hamiltonian system J ˙ x - u*A(t)u(x) + u*G'(t, u(x)) = 0, where the function G satisfies a new superquadratic condition which includes the case G(t, y) = |y|2(ln(1+|y|p))q, p, q > 1. By using a linking theorem, we obtain some new results.

Słowa kluczowe

EN

periodic solutions; Hamiltonian systems; critical point theory

PL

rozwiązania okresowe; układy hamiltonowskie; twierdzenie o punkcie krytycznym

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 331--346
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Timoumi M.

• Department Mathematiques-Faculte des Sciences 5000 Monastir-Tunisia

Bibliografia

• [1] G. Fournier, M. Timoumi, M. Willem, The limiting case for strongly indefinite functionals, Topol. Methods Nonlinear Anal. 1 (1993), 203-209.
• [2] S. Li, A. Szulkin, Periodic solutions for a class of nonautonomous Hamiltonian systems, J. Differential Equations (1994), 226-238.
• [3] S. Li, M.Willem, Applications of local linking to critical point theory, Rapport n. 203, January 1992, Seminaire mathematique, U.C.L.
• [4] P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. in Math, n0 65, Amer.Math. Soc., Providence R.I, 1986.
• [5] M. Timoumi, Oscillations de syst`emes hamiltoniens surquadratiques non coercitifs, Demonstratio Math. 27, N0 2 (1994), 293-300.
• [6] M. Willem, Lectures notes on critical point theory, Trabalho de Mat., 199, Funda Univ. Brasilia, 1983.