The Latin American School of Mathematics (ELAM) is one of the most important mathematical events in Latin America. It has been held every other year since 1968 in a different country of the region, and its theme varies according to the areas of interest of local research groups. The subject of the 1986 school was Partial Differential Equations with emphasis on Microlocal Analysis, Scattering Theory and the applications of Nonlinear Analysis to Elliptic Equations and Hamiltonian Systems.

Critical points at infinity in the variational calculus.- On the number of bound states and estimates on some geometric invariants.- Convergence of solutions of capillo-viscoelastic perturbations of the equations of elasticity.- Mathematical aspects of the minimum critical mass problem.- Asymptotic time evolutions for strictly outgoing multiparticle quantum systems with long-range potentials.- A "birkhoff-lewis" type result for non autonomous differential equations.- Nonresonance near the first eigenvalue of a second order elliptic problem.- Differential equations in the spectral parameter and multiphase similarity solutions.- Recent results on semi-linear hyperbolic problems in bounded domains.- Systems of homogeneous partial differential equations with few solutions.- to multiplicity theory for boundary value problems with asymmetric nonlinearities.- Regularity of solutions of cauchy problems with smooth cauchy data.- Necessary and sufficient condition for maximal hypoellipticity of .- Examples of non-discreteness for the interaction geometry of semilinear progressing waves in two space dimensions.- On the cauchy problem for hyperbolic equations in C? and gevrey classes.- Positivity and stability for cauchy problems with delay.- On the resonances and the inverse scattering problem for perturbed wave equations.- The initial value problem for euler and navier-stokes equations in L s p (?2).- Periodic solutions of prescribed energy of hamiltonian systems.- Semi-Classical approximations in solid state physics.- Microlocal analysis for inhomogeneous gevrey classes.- Estimates on the number of resonances for semiclassical schrödinger operators.- Heat-flow methods for harmonic maps of surfaces and applications to free boundary problems.- Inverse boundary valueproblems.- Scattering on the line - an overview.- Microlocal cohomology in hypo-analytic structures.