Nonlinear Differential Equations and Applications NoDEA

, Volume 6, Issue 3, pp 247–266

A Dual Variational Approach to a Class of Nonlocal Semilinear Tricomi Problems

  • Daniela Lupo
  • Kevin R. Payne

DOI: 10.1007/s000300050075

Cite this article as:
Lupo, D. & Payne, K. NoDEA, Nonlinear differ. equ. appl. (1999) 6: 247. doi:10.1007/s000300050075


The existence of at least one nontrivial solution to a class of semilinear Tricomi problems is established via an application of the dual variational method which captures the solution as the preimage of a minimum of a suitable dual action functional. The boundary conditions are homogeneous Dirichlet conditions on a suitable part of the boundary, as dictated by uniqueness theorems for the linear problem. While there are good compactness properties for the inverse operator for the linear problem, there is a manifest asymmetry in the linear part due to the form of the boundary conditions. The linear part is symmetrized by introducing suitable re ection operators on symmetric domains, which then results in a nonlocal character of the nonlinearity.

Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • Daniela Lupo
    • 1
  • Kevin R. Payne
    • 2
  1. 1.Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy, e-mail: danlup@mate.polimi.itIT
  2. 2.Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124-4250, USA, e-mail: