The Multiplicity of Solutions in Non-homogeneous Boundary Value Problems the Multiplicity of Solutions in Non-homogeneous Boundary Value Problems

We use a method recently devised by Bolle B] to establish the existence of an innnite number of solutions for various non-homogeneous boundary value problems. In particular, we consider second order systems, Hamiltonian systems as well as semi-linear partial diierential equations. The non-homogeneity can originate in the equation but also from the boundary conditions. The results are much more satisfactory than those obtained by the standard \Perturbation from Symmetry" method that was developed {in various forms{in the early eighties by Bahri-Berestycki, Struwe and Rabinowitz. 1. Introduction: Equivariant variational methods often yield multiple solutions for partial diierential equations and Hamiltonian systems that are invariant under certain group actions. However, there are not yet satisfactory general answers to the cases where the group symmetry is broken by some non-equivariant { and even linear{ perturbations. A partially successful method to deal with such problems was devised in the early eighties by Bahri-Berestycki Ba-Be1,2] and Struwe St]. The variational principle underlying these results was later formulated by Rabinowitz R]. The main idea being to think of the non-symmetric functional I under study as a perturbation of its symmetric part I 0 and then to estimate how the growth rate of the critical levels of I 0 is aaected by the perturbation from