Bifurcation techniques for a class of boundary value problems of fractional impulsive differential equations. (English) Zbl 1319.34013
Summary: This paper investigates the existence of positive solutions for a class of boundary value problems (BVP) of fractional impulsive differential equations and presents a number of new results. Firstly, by constructing a novel transformation, the considered impulsive system is convert into a continuous system. Secondly, using a specially constructed cone, the Krein-Rutman theorem, topological degree theory, and bifurcation techniques, some sufficient conditions are obtained for the existence of positive solutions to the considered BVP. Finally, an example is worked out to demonstrate the main result.
MSC:
34A08 | Fractional ordinary differential equations |
34B37 | Boundary value problems with impulses for ordinary differential equations |
34C23 | Bifurcation theory for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |
34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |