分数阶微分方程无穷多点边值问题正解的存在性

Existence of Positive Solutions for Fractional Differential Equationswith Infinite Multipoint Boundary Value Problems

考虑无穷多点边界条件下的一类Riemann-Liouville分数阶边值共振问题的可解性.首先,利用锥拉伸与压缩不动点定理,在非线性项f满足一定的条件下,得到了问题正解的存在性;其次,在非线性项f满足更强的条件下,利用Leggett-Williams不动点定理得到了3个正解的结果.

The author considered the solvability of a class of Riemann-Liouville fractional boundary value resonance problems with infinite multipoint boundary conditions.Firstly,by using the fixed point theorem of cone extension and compression,the author obtained the existence of a positive solution when the nonlinear term f satisfied a certain condition.Secondly,under the condition that the nonlinear term f satisfied stronger conditions,the results of three positive solutions of the problem were obtained by using Leggett-Williams fixed point theorem.