MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR

Yanqiong Lu; Ruyun Ma

doi:10.11948/20200033

2021 Volume 11 Issue 2

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Yanqiong Lu, Ruyun Ma. MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 841-857. doi: 10.11948/20200033

Citation:

Yanqiong Lu, Ruyun Ma. MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 841-857. doi: 10.11948/20200033

MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR

Yanqiong Lu^1, ,,
Ruyun Ma¹

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Corresponding author: Email: linmu8610@163.com(Y. Lu)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11901464, 11801453, 11671322) and the Young Teachers'Scientifc Research Capability Upgrading project of Northwest Normal University(NWNU-LKQN2020-20)

Abstract

Abstract

We shall discuss the existence and multiplicity of positive solutions for the discrete Dirichlet problem with one-dimensional prescribed mean curvature operator. Based on the critical point theory, we shall show the existence of either one, or two, or three, or infinity many positive solutions depending on the asymptotic behavior of nonlinearity near zero.
- Positive solutions /
- multiplicity /
- prescribed mean curvature operator /
- critical point theory
MSC: 34B15, 34B18

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References

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