Variational approaches to p-Laplacian discrete problems of Kirchhoff-type

Abstract

Critical point results for Kirchhoff-type discrete boundary value problems are exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behaviour of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behaviour of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.

Keywords:

• Nonlinear difference equations
• discrete boundary value problem
• Kirchhoff-type problem
• one solution
• infinitely many solutions
• variational methods
• critical point theory

AMS Subject Classifications:

• 39A05
• 34B15
• 74H10
• 74H20
• 74H60
• 92D25

Notes

No potential conflict of interest was reported by the authors.