Bifurcation type phenomena for positive solutions of a class of impulsive differential equations.

In this paper, we are concerned with the existence, nonexistence, and multiplicity of positive solutions for a impulsive periodic boundary value problem with positive parameter λ$$ \lambda $$. Using the critical point theorem, we obtain a bifurcation type result about positive solutions; that is, there exists 0<Λ<∞$$ 0<\Lambda <\infty $$ such that our problem has at least two positive solutions for all λ∈(0,Λ)$$ \lambda \in \left(0,\Lambda \right) $$, one positive solution for λ=Λ$$ \lambda =\Lambda $$, and no positive solution for λ>Λ$$ \lambda >\Lambda $$ under the appropriate conditions. [ABSTRACT FROM AUTHOR]