An estimate for certain functional and its application

Author:

Gintaras PURIUŠKIS

2010 Mathematics Subject Classication:

35Q41

Keywords:

blow up, estimation, functional, periodic solution, Schrödinger equation.

Abstract:

We consider the functional \max_{j=0,1,2,3} \|f^{(j)}\|_{L^{\infty}(0,T)}, where f is a polynomial of sixth degree satisfying the boundary conditions f^{(j)}(0)=a_j, f^{(j)}(T)=0, j=0,1,2, and find the minimum of this functional. We also apply this minimum for determination of blow up conditions of the solution of the periodic nonlinear Schrödinger equation.

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Puri-2011

Vol. 6 (14), 2011