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Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space

  • Zhiqian He EMAIL logo and Liangying Miao

Abstract

In this paper, we study the number of classical positive radial solutions for Dirichlet problems of type

(P) d i v u 1 | u | 2 = λ f ( u ) in B 1 , u = 0 on B 1 ,

where λ is a positive parameter, B 1 = { x R N : | x | < 1 } , f : [0, ∞) → [0, ∞) is a continuous function. Using the fixed point index in a cone, we prove the results on both uniqueness and multiplicity of positive radial solutions of (P).

2010 Mathematics Subject Classification: 34B18; 35J60; 47H11; 47H07

Corresponding author: Zhiqian He, Department of Basic Teaching and Research, Qinghai University, Xining 810016, P. R. China, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Supported by the Natural Science Foundation of Qinghai Province (2021-ZJ-957Q), the National Natural Science Foundation of China (No. 11671322).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-05-21
Accepted: 2021-07-20
Published Online: 2021-08-05
Published in Print: 2022-12-16

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