scholarly journals Monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations: local moving planes and unique continuation in a non-Lipschitz case

2004 ◽  
Vol 58 (3-4) ◽  
pp. 299-317 ◽  
Author(s):  
Jean Dolbeault ◽  
Patricio Felmer
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Unique Continuation ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Moving Planes

scholarly journals Some notes on the method of moving planes

1992 ◽  
Vol 46 (3) ◽  
pp. 425-434 ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Nonlinear Elliptic Equations ◽  
Smoothness Condition ◽  
Plane Method ◽  
Nonlinear Elliptic ◽  
Method Of Moving Planes ◽  
Moving Planes

In this paper, we obtain a version of the sliding plane method of Gidas, Ni and Nirenberg which applies to domains with no smoothness condition on the boundary. The method obtains results on the symmetry of positive solutions of boundary value problems for nonlinear elliptic equations. We also show how our techniques apply to some problems on half spaces.

Solutions with multiple peaks for nonlinear elliptic equations

1999 ◽  
Vol 129 (2) ◽  
pp. 235-264 ◽  
Author(s):  
Daomin Cao ◽  
Ezzat S. Noussair ◽  
Shusen Yan
Keyword(s):  
Positive Solutions ◽  
Critical Points ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Multiple Peaks ◽  
Nonlinear Elliptic ◽  
Image Position

Solutions with peaks near the critical points of Q(x) are constructed for the problemWe establish the existence of 2k −1 positive solutions when Q(x) has k non-degenerate critical points in ℝN

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