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Étude des solutions généralisées pour un système hamiltonien avec potentiel singulier. (Study of generalized solutions for a Hamiltonian system with singular potential). (French) Zbl 0758.35016

The author studies the generalized solutions of the Hamiltonian system: \(\ddot q=-V_ q'(q,t)\) where the potential \(V\) is singular and has a particular expression.

MSC:

35D05 Existence of generalized solutions of PDE (MSC2000)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

[1] A. Bahri and P. H. Rabinowitz, A minimax method for a class of Hamiltonian systems with singular potentials , J. Funct. Anal. 82 (1989), no. 2, 412-428. · Zbl 0681.70018
[2] C. Greco, Remarks on periodic solutions for some dynamical systems with singularities , Periodic solutions of Hamiltonian systems and related topics (Il Ciocco, 1986) ed. P. H. Rabinowitz, et al., NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 209, Reidel, Dordrecht, 1987, pp. 169-173. · Zbl 0632.34043
[3] C. Greco, Periodic solutions of a class of singular Hamiltonian systems , Nonlinear Anal. 12 (1988), no. 3, 259-269. · Zbl 0648.34048
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