Positive solutions of partial discrete Kirchhoff type problems

Abstract

In this paper, by using critical point theory, we study the infinitely many solutions of partial discrete Kirchhoff type problems. Moreover, we acquire some sufficient conditions for the existence of positive solutions to the boundary value problems by using the strong maximum principle. As far as we know, this is the research of partial discrete Kirchhoff type problems for the first time. Finally, our major results are explained with four examples.

Keywords

• Kirchhoff type problem
• Infinitely many solutions
• Partial difference equation
• Critical point theory