The existence of at least one nontrivial solution to a class of semi- linear 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 reflection operators on symmetric domains, which then results in a nonlocal character of the nonlinearity.

A Dual Variational Approach to a Class of Nonlocal Semilinear Tricomi Problems / D. Lupo, K.R. Payne. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 6:3(1999), pp. 247-266.

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

K.R. Payne
Ultimo
1999

Abstract

The existence of at least one nontrivial solution to a class of semi- linear 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 reflection operators on symmetric domains, which then results in a nonlocal character of the nonlinearity.
Analysis; Applied Mathematics
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/451779
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