NONLINEAR SCHRODINGER EQUATIONS ON PERIODIC METRIC GRAPHS

作者：Pankov Alexander^*

来源：Discrete and Continuous Dynamical Systems, 2018, 38(2): 697-714.

DOI：10.3934/dcds.2018030

• Metric graph
• periodic nonlinear Schrodinger equation
• generalized Nehari manifold
• periodic approximation

The paper is devoted to the nonlinear Schrodinger equation with periodic linear and nonlinear potentials on periodic metric graphs. Assuming that the spectrum of linear part does not contain zero, we prove the existence of finite energy ground state solution which decays exponentially fast at in finity. The proof is variational and makes use of the generalized Nehari manifold for the energy functional combined with periodic approximations. Actually, a finite energy ground state solution is obtained from periodic solutions in the in finite wave length limit.

• 出版日期2018-2