Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space

Article type: Research Article

Authors: Dai, Guowei^a | Zhang, Zhitao^{b; c; d; *}

Affiliations: [a] School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China | [b] School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P.R. China | [c] Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, P.R. China | [d] School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China

Correspondence: [*] Corresponding author. E-mail: zzt@math.ac.cn.

Abstract: By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime rN−kv′1−v′2k′=λNCNkrN−1Hk(r,v)in (0,R),|v′|<1in (0,R),v′(0)=v(R)=0. As a previous step, we investigate the spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the asymptotic behaviors of solutions with respect to λ.

Keywords: Spectrum, Bifurcation, k-th mean curvature, Nodal solutions, A priori bounds, Asymptotic behaviors, One-sign solution

DOI: 10.3233/ASY-231877

Journal: Asymptotic Analysis, vol. 136, no. 3-4, pp. 257-289, 2024