On the Necessary and Sufficient Condition of Existence of Solution to Cauchy problem of a Class of Degenerate Equation

【摘要】 <正> In this paper, we discuss the existence of the solution to the Cauchy problem: L_p^ku≡u_xx-x^2ku_tt+Px^k-1u_t=f（x,t）,t≥0, （1） （A_k） u（x,0）=ψ₁（x）, u_t（x,0）=ψ₂（x）, （2）where κ=2i+1, i=0,1,2,…,P R=（-∞, +∞）, ψ₁（x）,ψ₂（x）∈C^∞（R）, f（x,t） ∈C^∞（R₂⁺）,R₂⁺={（x, t）∈R²|t≥0}.If κ=1, the uniqueness and existence of solution to the Cauchy problem（A_κ） was entirely solved by [1-3], if κ>1, A. Menikoff proved that the C^∞更多还原