非线性奇异边值问题的正解

Positive Solutions of Singular Boundary Value Problems of Differential Equations

该文利用锥上的不动点定理,在较弱的条件下,讨论了非线性Sturm-Liouville方程奇异边值问题正解的存在性,并获得了当特征值λ在某一范围内取值时,边值问题至少存在一个正解的结论.作者的结果包含、推广并改进了许多已知的结果.

The authors consider the existence of positive solutions for the singular boundary value problem using fixed point theory in cones, the authors derive an explicit interval for ,λ such that for any ,λ in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed. The results significantly extend and improve many known results even for non-singular cases.