Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

Shaohong Wang and Zhan Zhou
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Shaohong Wang: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Zhan Zhou: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Mathematics, 2021, vol. 9, issue 14, 1-20

Abstract: Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.

Keywords: Dirichlet boundary value problem; partial difference equation; the mean curvature operator; critical point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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