Some new findings on bounded solution of a third order iterative boundary-value problem

Abstract

This article investigates a boundary value problem for a third-order iterative differential equation. Under certain conditions and by employing Schauder’s fixed point theorem, we establish some new results on the existence, uniqueness and continuous dependence of bounded solutions of the proposed problem. An example is presented to highlight the effectiveness of the derived results which are completely new and form a complement to some existent studies to some extent.

Subject Classification: (2010):

• 34A12
• 34B15
• 39B12
• 47H10

Keywords:

• Boundary value problems
• Continuous dependence
• Fixed point theorems
• Iterative equations