scholarly journals Existence and continuation of solutions for a nonlinear Neumann problem

2008 ◽  
Vol 69 (10) ◽  
pp. 3423-3449 ◽  
Author(s):  
Krzysztof Muchewicz ◽  
Sławomir Rybicki
Keyword(s):  
Neumann Problem ◽  
Nonlinear Neumann Problem

scholarly journals Solvability of a nonlinear Neumann problem for systems arising from a burglary model

2014 ◽  
Vol 35 ◽  
pp. 102-108 ◽  
Author(s):  
M. Garcia-Huidobro ◽  
R. Manásevich ◽  
J. Mawhin
Keyword(s):  
Neumann Problem ◽  
Nonlinear Neumann Problem

Multiple Solutions for Nonlinear Neumann Problems with Asymmetric Reaction, via Morse Theory

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Variational Methods ◽  
Neumann Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Smooth Solutions ◽  
Asymmetric Reaction ◽  
Neumann Problems ◽  
Nonlinear Neumann Problem ◽  
Asymmetric Behaviour ◽  
Nonlinear Neumann Problems

AbstractWe consider a nonlinear Neumann problem driven by the p-Laplacian and with a reaction which exhibits an asymmetric behaviour near +∞ and near −∞. Namely, it is (p − 1)- superlinear near +∞ (but need not satisfy the Ambrosetti-Rabinowitz condition) and it is (p − 1)-linear near −∞. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions.

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