Bull. Korean Math. Soc. 2024; 61(1): 29-44
Online first article January 19, 2024 Printed January 31, 2024
https://doi.org/10.4134/BKMS.b230001
Copyright © The Korean Mathematical Society.
Man Xu
Northwest Normal University
In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to $+\infty$. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.
Keywords: Higher mean curvature spacelike equation, Minkowski spacetime, rotationally symmetric solutions, topological degree, prolongability theorem
MSC numbers: Primary 34B16, 34B18, 35B08, 35J93
Supported by: This work was supported by the NSFC (No.11671322) and by the grant 21JR1RA230, 2021A-006 and NWNU-LKQN2021-17.
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