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The multiplicity of solutions in non-homogeneous boundary value problems
Authors:Phillipe Bolle  Nassif Ghoussoub  Hossein Tehrani
Institution:(1) CEREMADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France, FR;(2) Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada, CA;(3) Department of Mathematics, University of Nevada, Las Vegas, NV 89154, USA, US
Abstract:We use a method recently devised by Bolle to establish the existence of an infinite 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 differential equations. The non-homogeneity can originate in the equation but also from the boundary conditions. The results are 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. Received: 13 August 1998 / Revised version: 6 July 1999
Keywords:Mathematics Subject Classification (1991):35B40  35B45  58E05  Secundary 35J40
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