具变号权函数的多参数二阶微分系统多个正解的存在性
Existence of Multiple Positive Solutions for Multi-Parameter Second-Order Differential Systems with Indefinite Weight Functions
摘要: 本文研究了一类具变号权函数的多参数二阶微分系统多个正解的存在性。根据参数λ和μ的不同取值，并结合范数形式的锥拉伸与压缩不动点定理，得到了二阶微分系统至少存在两个正解和三个正解的结果。最后，通过例子验证定理的条件是合理的。
Abstract: This paper investigates the existence of multiple positive solutions for a class of multi-parameter second-order differential systems with indefinite weight functions. According to the different values of parameters λ and μ, and combining fixed-point theorem of cone expansion and compression of norm type, the results of at least two positive solutions and three positive solutions for the second-order differential systems are established. Finally, two examples are included to illustrate the rationality of the assumptions of obtained theorems.
文章引用：秦培歌, 薛春艳. 具变号权函数的多参数二阶微分系统多个正解的存在性[J]. 理论数学, 2018, 8(4): 411-425. https://doi.org/10.12677/PM.2018.84055

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