一类具不变性质的变系数偏微分方程的特解

In this paper, a few properties of general patial differential operator P beinginvariant with respect to the form F(|x|_p^p+|y|_q^q-|z|_r^r) are studied, where x∈Rⁿ,y∈ R^m, z∈R^l.and explicit formulas are given for certain solution of the equation Pu=Aδ with P being a differential operator with power function coefficientswhich preserves the form (|x|_p^p+|y|_q^q-|z|_r^r)^1/v for arbitrary even integers p, q, r,and odd integers v.

Particular Solutions of a Class of Partial Differential Equations with Variate Coefficients and Invariant Properties