一类二阶奇异拟线性方程的解和正解
Solutions and Positive Solution of a Class of Second-Order Singular Quasilinear Equations
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摘要: 考察了一类含有一阶导数的二阶拟线性方程的解和正解,其中允许非线性项是奇异的。通过构造适当的Banach空间并利用相应的积分方程建立了两个局部存在定理。这些定理表明解和正解的存在性取决于非线性项的主要部分在某个集合上的“高度”。Abstract: The solution and positive solution are considered for a class of second-order quasilinear equations with first derivative,where the nonlinear term is allowed to be singular.By constructing suitable Banach space and applying corresponding integral equation,two local existence theorems are established. The theorems show that the existence of solution and positive solution depends upon the "height" of principal part of nonlinear term on a bounded set.