scholarly journals Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential

2008 ◽  
Vol 19 (2) ◽  
pp. 95-131 ◽  
Author(s):  
Tomáš Dohnal ◽  
Dmitry Pelinovsky ◽  
Guido Schneider
Keyword(s):  
Elliptic Problem ◽  
Periodic Potential ◽  
Two Dimensional ◽  
Nonlinear Elliptic Problem ◽  
Coupled Mode ◽  
Nonlinear Elliptic ◽  
Gap Solitons

scholarly journals On the Existence of Nodal Solutions for a Nonlinear Elliptic Problem on Symmetric Riemannian Manifolds

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Multiplicity Result ◽  
Nonlinear Elliptic Problem ◽  
Nodal Solutions ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions

Given thatis a smooth compact and symmetric Riemannian -manifold, , we prove a multiplicity result for antisymmetric sign changing solutions of the problem in . Here if and if .

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