带一般微分算子的二阶奇异边值问题的正解

摘要

用锥拉伸与压缩不动点定理,研究带一般微分算子的二阶奇异边值问题,其中线性微分算子的函数系数也允许具有奇异性.在非线性项满足超线性或次线性条件下,得到了该问题至少存在一个正解,并给出一个实例检验所得结果的有效性.%By using the fixed point theorem of cone expansion and compression,we studied the second-order singular boundary value problem with general differential operator,in which the coefficients of linear differential operator were also allowed to be singular.We obtained the existence result of at least one positive solution under the nonlinearity satisfying either superlinear or sublinear conditions, and gave an example to test the validity of the result.