On decay of solutions to nonlinear Schrödinger equations

Pankov, Alexander

doi:10.1090/S0002-9939-08-09484-7

On decay of solutions to nonlinear Schrödinger equations
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Proc. Amer. Math. Soc. 136 (2008), 2565-2570 Request permission

Abstract:

We present general results on exponential decay of finite energy solutions to stationary nonlinear Schrödinger equations. Under certain natural assumptions we show that any such solution is continuous and vanishes at infinity. This allows us to interpret the solution as a finite multiplicity eigenfunction of a certain linear Schrödinger operator and, hence, apply well-known results on the decay of eigenfunctions.

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