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Multiplicity of Solutions for Non-homogeneous Dirichlet Problem with One-Dimension Minkowski-Curvature Operator

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Abstract

In this work, we study the multiplicity of solutions for non-homogeneous Dirichlet problem with one-dimension Minkowski-curvature operator

$$\begin{aligned} \Bigg (\frac{u'}{\sqrt{1-\kappa u'^2}}\Bigg )'+f(u)=0,\ t\in (0,1),\ \ \qquad u(0)=sA,\quad u(1)=sB, \end{aligned}$$

where \(\kappa >0\) is a constant, \(A,B\in {\mathbb {R}}\) are constants, \(s\in {\mathbb {R}}\) is a parameter and \(f:[0,\infty )\rightarrow {\mathbb {R}}\) is continuous. The results depend on the values of the real numbers s, A, B and on the behaviour of f(u)/u for u near zero.

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Data Availibility Statement

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This paper was supported by National Natural Science Foundation of China (Nos. 11901464, 11801453) and the Young Teachers’ Scientific Research Capability Upgrading Project of Northwest Normal University(No. NWNU-LKQN2020-20). The authors are very grateful to the reviewers for their valuable suggestions.

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

    Yanqiong Lu, Zhiqiang Li & Tianlan Chen

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  1. Yanqiong Lu
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We certify that this manuscript is original and has not been published and will not be submitted elsewhere for publication while being considered by Qualitative Theory of Dynamical Systems. And the study is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time. No data have been fabricated or manipulated (including images) to support our conclusions. No data, text, or theories by others are presented as if they were our own. This article does not contain any studies with human participants or animals.

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Lu, Y., Li, Z. & Chen, T. Multiplicity of Solutions for Non-homogeneous Dirichlet Problem with One-Dimension Minkowski-Curvature Operator. Qual. Theory Dyn. Syst. 21, 145 (2022). https://doi.org/10.1007/s12346-022-00675-x

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