Positive solutions of the discrete Robin problem with $ \phi $-Laplacian

Jiaoxiu Ling; Zhan Zhou

doi:10.3934/dcdss.2020338

Article Contents

2021, Volume 14, Issue 9: 3183-3196. Doi: 10.3934/dcdss.2020338

This issue Previous Article On the number of limit cycles of a quartic polynomial system Next Article Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting

Positive solutions of the discrete Robin problem with $ \phi $-Laplacian

Jiaoxiu Ling^1,2, and
Zhan Zhou^1,2, ,

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2.
Center for Applied Mathematics Guangzhou University Guangzhou 510006, China

^* Corresponding author: Zhan Zhou
^* Corresponding author: Zhan Zhou

Received: March 31, 2019

Revised: September 30, 2019

Early access: April 2020

Published: September 2021

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Abstract

In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the discrete Robin problem with $ \phi $-Laplacian. We show that, an unbounded sequence of positive solutions and a sequence of positive solutions which converges to zero will emerge from the suitable oscillating behavior of the nonlinear term at infinity and at the zero, respectively. We also give two examples to illustrate our main results.

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Mathematics Subject Classification: 39A12.

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