s of Plenary Talks 16 Abstracts of Invited Talks 18s of Invited Talks 18 Abstracts of Contributed Talks 35s of Contributed Talks 35 Index of Participants 51

A new and simpler proof is given of the result of P. Rabinowitz for nontrivial time periodic solutions of a vibrating string equation utt-ux, + g(u) = 0 and Dirichlet boundary conditions on a finite interval. We assume essentially that g is nondecreasing, and g(u)/u+m as Iu(+w. The proof uses a modified form (PS), of the Palais-Smale condition (PS). Let g : R-+R be a continuous nondecreasing fu...

Let f be a positive smooth function on a close Riemann surface (M,g). The f − energy of a map u from M to a Riemannian manifold (N, h) is defined as E f (u) = M f |∇u| 2 dV g. In this paper, we will study the blow-up properties of Palais-Smale sequences for E f. We will show that, if a Palais-Smale sequence is not compact, then it must blows up at some critical points of f. As a sequence, if an...

It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict th...

We consider a class of variational systems in R N of the form where a; b : R N ! R are continuous functions which are coercive; i.e., a(x) and b(x) approach plus innnity as x approaches plus innnity. Under appropriate growth and regularity conditions on the nonlinearities Fu(:) and Fv (:), the (weak) solutions are precisely the critical points of a related functional deened on a Hilbert space o...