Positive and decreasing solutions for higher order Caputo boundary valueproblems with sign-changing Green’s function

Abstract

: In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0 , 1] . By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results.