On a prescribed mean curvature equation in Lorentz-Minkowski space

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• 作者：A. Azzollini¹ ; ^{antonio.azzollini@unibas.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J62 ; 35J93 ; 35A24
• 刊名：Journal de mathematiques pures et appliquees
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：106
• 期：6
• 页码：1122-1140
• 全文大小：449 K

文摘

We are interested in providing new results on the following prescribed mean curvature equation in Lorentz–Minkowski space set in the whole R^N${\mathbb{R}}^N$, with N⩾3$N⩾3$.

We study both existence and multiplicity of radial ground state solutions (namely positive and vanishing at infinity) for p>1$p>1$, emphasizing the fundamental difference between the subcritical and the supercritical case.

We also study speed decay at infinity of ground states, and give some decay estimates.

Finally we provide a multiplicity result on the existence of sign-changing bound state solutions for any p>1$p>1$.