Electron. J. Diff. Eqns., Vol. 1999(1999), No. 29, pp. 1-11.

Solutions to elliptic systems of Hamiltonian type in ${\Bbb R}^N$

K. Tintarev

The paper proves existence of a solution for elliptic systems of Hamiltonian type on ${\Bbb R}^N$ by a variational method. We use the Benci-Rabinowitz technique, which cannot be applied here directly for lack of compactness. However, a concentration compactness technique allows us to construct a finite-dimensional pseudogradient that restores the Benci-Rabinowitz method to power also for problems on unbounded domains.

Submitted December 8, 1998. Published September 9, 1999.
Math Subject Classifications: 35J50.
Key Words: cocentration compactness, elliptic systems, pseudogradient.

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Kyril Tintarev
Department of Mathematics
Uppsala University
Box 480, Uppsala 751 06, Sweden
email: kyril@math.uu.se

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