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

Abstract

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<normalΛ<∞$$ 0&lt;\Lambda &lt;\infty $$ such that our problem has at least two positive solutions for all λ∈false(0,normalΛfalse)$$ \lambda \in \left(0,\Lambda \right) $$, one positive solution for λ=normalΛ$$ \lambda &#x0003D;\Lambda $$, and no positive solution for λ>normalΛ$$ \lambda &gt;\Lambda $$ under the appropriate conditions.