For small L2 norms the mass-supercritical Schrödinger equation with radial potential admits two solutions.
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Under a local second-order strict positivity condition on stationary equilibria, mean field game systems with quadratic Hamiltonians exhibit an exponential turnpike property near those equilibria on tori and Euclidean space, with existence of stable solutions established via fixed-point methods.
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Normalized solutions to mass supercritical Schr\"odinger equations with radial potentials
For small L2 norms the mass-supercritical Schrödinger equation with radial potential admits two solutions.
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The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian
Under a local second-order strict positivity condition on stationary equilibria, mean field game systems with quadratic Hamiltonians exhibit an exponential turnpike property near those equilibria on tori and Euclidean space, with existence of stable solutions established via fixed-point methods.