Oscillating solutions for prescribed mean curvature equations: Euclidean\n and Lorentz-Minkowski cases

2017/09/20 by Alessio Pomponio, Pomponio, Alessio
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1709.06980

Abstract

This paper deals with the prescribed mean curvature equations both in the\nEuclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity\ng such that g'(0)>0. We show the existence of oscillating solutions, namely\nwith an unbounded sequence of zeros. We show the existence of oscillating\nsolutions, namely with an unbounded sequence of zeros. Moreover these solutions\nare periodic, if N=1, while they are radial symmetric and decay to zero at\ninfinity with their derivatives, if N\≥ 2.\n

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