Non-uniqueness in the Cauchy problem for partial differential operators with multiple characteristics. II (Q5903661)

[For Part I see Commun. Partial Differ. Equations 9, 63-106 (1984; Zbl 0559.35001).] This paper is concerned with nonuniqueness in the Cauchy problem for a class of differential operators including the operator \[ P=(\partial_ t-it^{\ell}C(t,x)\partial_ x)^ p+t^ kA(t,x)(i\partial_ x)^ q- t^ mB(t,x)(i\partial_ x)^{q-r},\quad p\geq q>r\geq 1. \] Under some conditions the author shows that there exists a \(C^{\infty}\) function u flat on \(t=0\) and a function \(a\in C^{\infty}\) such that \(Pu+au=0\), (0,0)\(\in \sup p u\). These results were announced by the author in part I.