Strong instability of standing waves for nonlinear Schrodinger equations with a delta potential (Harmonic Analysis and Nonlinear Partial Differential Equations)

"Harmonic Analysis and Nonlinear Partial Differential Equations". June 30～July 2, 2014. edited by Hideo Kubo and Mitsuru Sugimoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We study strong instability (instability by blowup) of standing wave solutions for a nonlinear Schrödinger equation with an attractive delta potential and L^{2}-supercritical power nonlinearity in one space dimension. We also compare our sufficient condition on strong instability with some known results on orbital instability