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January  2008, 21(1): 187-220. doi: 10.3934/dcds.2008.21.187

Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems

Nassif Ghoussoub 1,

1. 

Department of Mathematics, The University of British Columbia, Vancouver BC Canada V6T 1Z2

Received  March 2007 Published  February 2008

Selfdual variational theory -- developed in [8] and [9] -- allows for the superposition of appropriate "boundary" Lagrangians with "interior" Lagrangians, leading to a variational formulation and resolution of problems with various linear and nonlinear boundary constraints that are not amenable to standard Euler-Lagrange theory. The superposition of several selfdual Lagrangians is also possible in many natural settings, leading to a variational resolution of certain differential systems. These results are applied to nonlinear transport equations with prescribed exit values, Lagrangian intersections of convex-concave Hamiltonian systems, initial-value problems of dissipative systems, as well as evolution equations with periodic and anti-periodic solutions.
Keywords: Selfdual functionals, boundary value and initial-value problems..
Mathematics Subject Classification: Primary: 35F10, 35J65; Secondary: 47N10, 58E3.
Citation: Nassif Ghoussoub. Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 187-220. doi: 10.3934/dcds.2008.21.187
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