L^p_c-concentration of blow-up solutions for the biharmonic nonlinear Schrödinger equation

Abstract

This article is concerned with the blow-up solutions of the biharmonic Schrödinger equation with L ²-super critical nonlinearity. We obtain the nonexistence of strong limit of L ^{p _c} -norm and L ^{p _c} -concentration properties of the radially symmetric blow-up solutions, where L ^{p _c} is the invariant Lebesgue space.

Keywords:

• biharmonic nonlinear Schrödinger equation
• blow-up solution
• L ^{p _c} -Concentration

AMS Subject Classifications::

• 35Q55
• 35B44

Acknowledgement

This research was supported by National Natural Science Foundation of P.R. China (No. 10771151) and Fundamental Research Funds for the Central Universities (SWJTU09ZX073 and SWJTU09ZT36).