On the uniqueness theorem for nonlinear singular partial diferential equations

Abstract. The paper proves a uniqueness theorem of the solution of nonlinear singular partial differential equations (t∂/∂t)mu = F t, x, {(t∂/∂t)j(∂/∂x)αu}j+|α|≤m,j<m If the characteristic exponents λ1(x),..., λm(x) of the equation satisfy the condition Reλi(0) < 0 for i = 1,...,m, a uniqueness theorem was proved in Tahara [6]. The present paper discusses the case where Reλi(x) ≤ 0 holds in a neighborhood of x = 0 for i = 1,...,m. The result is applied to the problem of removable singularities of the solution