带平均曲率算子的离散混合边值问题凸解的存在性

Abstract

Abstract:

In this paper, by using the fixed point theorem in cones, we discuss the existence of $ \Delta[\phi(\Delta v(t-1))]=f(t, -v(t)), {\quad} t\in[2, T-1]_{{\Bbb Z}}, $ $ \Delta v(1)=0, {\quad} v(T)=0 $ nontrivial convex solutions for a discrete mixed boundary value problem of mean curvature operator in Minkowski space, where $ \phi(s)=\frac{s}{\sqrt{1-s^{2}}}, s\in(-1, 1), $ $ [2, T-1]_{{\Bbb Z}}:=\{2, 3, \cdots, T-2, $ $ T-1\}, $ $ T\geqslant4 $ and $ T\in{\Bbb N}^{\ast} $, the nonlinear term $ f(t, u) $ is nonnegative and continuous, and singularity is allowed at $ u=1 $.

Key words: Mean curvature operator, Discrete mixed boundary value problem, Nontrivial convex solutions, Cone, Fixed point theorem

CLC Number:

O175.7

Lei Duan,Tianlan Chen. Existence of Convex Solutions for a Discrete Mixed Boundary Value Problem with the Mean Curvature Operator[J].Acta mathematica scientia,Series A, 2022, 42(2): 379-386.

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References 16

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Existence of Convex Solutions for a Discrete Mixed Boundary Value Problem with the Mean Curvature Operator

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