abstract: The aim of this talk is to demonstrate eectiveness of extension theory for investigation of stability of standing waves for semi-linear Schrodinger equation with - and 0 -interaction. Our approach relies on the abstract theory by Grillakis, Shatah and Strauss for Hamiltonian systems which are invariant under a one-parameter group of operators. This is joint work with Nataly GoloshchapovaDepartment of Mathematics, IME-USP