L2 Concentration of Blow-Up Solutions for the Nonlinear Schrödinger Equation with an Inhomogeneous Combined Non-Linearity

This article studies the Schrodinger equation with an inhomogeneous combined term i partial derivative(t)u-(-Delta)(s)u+lambda(1)|x|(-b)|u|(p)u+lambda(2)|u|(q)u=0, where s is an element of(1/2,1), lambda(1),lambda(2 )=+/- 1,0< b< {2s,N} and p, q> 0. We study the limit behaviour of the infinite blow-up solution at the blow-up time. When the parameters p,q,lambda(1) and lambda(2) have different values, we obtain the nonexistence of a strong limit for the non-radial solution and the L-2 concentration for the radial solution. Interestingly, we find that the mass of the finite time blow-up solutions are concentrated in different ways for different parameters.