Abstract
We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques.
Highlights
Fractional differential equations have been extensively studied in recent years
What if the boundary value conditions are nonlocal rather than local? Can we add impulsive terms into the system? As a reply to above questions, we will tackle the following impulsive Caputo fractional differential equations attached with integral boundary value conditions in this paper
To verify the existence of at least one positive solution of (2), we only need to show that C+ crosses the hyperplane {1}× X in R×X
Summary
Fractional differential equations have been extensively studied in recent years (see, for instance, [1–7] and their references). Since Rabinowitz established unilateral global bifurcation theorems, there have been many researches in global bifurcation theory and it has been applied to obtain the existence and multiplicity for solutions of differential equations (see, for instance, [8–16] and their references). The previous researches seldom involve both global bifurcation techniques and fractional differential equations. In [16], the following problem was studied. As a reply to above questions, we will tackle the following impulsive Caputo fractional differential equations attached with integral boundary value conditions in this paper. An appendix is given to prove a formula which will be used in the proof of the main results
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