Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation
Abstract
A functional proposed by Choquard (1976) in an approximation to the Hartree-Fock theory of a one-component plasma is studied. The difficulty in minimizing the functional stems from the fact that it lacks convexity. Existence and uniqueness of a minimizing function for the functional satisfying a nonlinear Schroedinger equation are proved. The proofs make use of the theory of symmetric decreasing functions, with a strict form of the inequality being employed for the uniqueness proof.
- Publication:
-
Studies in Applied Mathematics
- Pub Date:
- October 1977
- Bibcode:
- 1977StAM...57...93L
- Keywords:
-
- Hartree Approximation;
- Nonlinear Equations;
- Plasma Physics;
- Schroedinger Equation;
- Analysis (Mathematics);
- Convexity;
- Electrons;
- Existence Theorems;
- Inequalities;
- Minima;
- Symmetry;
- Uniqueness Theorem;
- Plasma Physics