This issuePrevious ArticleSchrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing wavesNext ArticleExistence of radial solutions for an elliptic problem involving exponential nonlinearities
Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems
Selfdual variational theory -- developed in  and  -- 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.