Periodic boundary value problems for first order difference equations

Abstract

In this paper, existence criteria for single and multiple positive solutions of some of periodic boundary value problems for first order difference equation \[\left\{\begin{array}{ll} \Delta x(k)+f(k,x(k+1))=0, & k\in \left[ 0,T\right] ,\\ x(0)=x(T+1), & \end{array}\right.\] are established by using the fixed point theorem in cones. An example is also given to illustrate the main results.

Keywords

• periodic boundary value problem
• positive solution
• fixed point theorem
• difference equation
• cone