Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for N ≥ 3

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• 作者：Jesús Ildefonso Díaz ; Jesús Hernández…
• 关键词：Semilinear elliptic and parabolic equation ; Strong absorption ; Spectral problem ; Nehari manifolds ; Pohozaev identity ; Flat solution ; Linearized stability ; Lyapunov function ; Global instability
• 刊名：Chinese Annals of Mathematics, Series B
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：38
• 期：1
• 页码：345-378
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1860-6261
• 卷排序：38

文摘

The authors prove that flat ground state solutions (i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1,2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.