On a semilinear variational problem
Bernd Schmidt (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We provide a detailed analysis of the minimizers of the functional , , subject to the constraint . This problem, , describes the long-time behavior of the parabolic Anderson in probability theory or ground state solutions of a nonlinear Schrödinger equation. While existence can be proved with standard methods, we show that the usual uniqueness results obtained with PDE-methods can be considerably simplified by additional variational arguments. In addition, we investigate qualitative...