Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains

作者：Moroz Vitaly^*; Van Schaftingen Jean

来源：Journal of Differential Equations, 2013, 254(8): 3089-3145.

DOI：10.1016/j.jde.2012.12.019

• Stationary Choquard equation
• Stationary focusing Hartree equation
• Stationary nonlinear Schrodinger-Newton equation
• Riesz potential
• Nonlocal semilinear elliptic problem
• Exterior domain
• Nontrivial nonnegative supersolutions
• Ground-state transformation
• Decay estimates
• Nonlinear Liouville theorems

We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schrodinger-Newton equation. We show that for some values of the parameters the equation does not have nontrivial nonnegative supersolutions in exterior domains. The same techniques yield optimal decay rates when supersolutions exist.

• 出版日期2013-4-15