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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 $\begin{matrix} \{\begin{array}{ll} {(r^{N - k} {(\frac{v^{'}}{\sqrt{1 - v^{' 2}}})}^{k})}^{'} = λ \frac{N}{C_{N}^{k}} r^{N - 1} H_{k} (r, v) & in (0, R), \\ | v^{'} | < 1 & in (0, R), \\ v^{'} (0) = v (R) = 0 . \end{array} \end{matrix}$ 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 Nodal solutions A priori bounds Asymptotic behaviors One-sign solution

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

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