scholarly journals Anisotropic nonlinear Neumann problems

2011 ◽  
Vol 42 (3-4) ◽  
pp. 323-354 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Neumann Problems ◽  
Nonlinear Neumann Problems

Coercive and noncoercive nonlinear Neumann problems with indefinite potential

2016 ◽  
Vol 28 (3) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Differential Operator ◽  
Neumann Problems ◽  
Nonhomogeneous Differential Operator ◽  
Indefinite Potential ◽  
Nonlinear Neumann Problems

AbstractWe consider nonlinear Neumann problems driven by a nonhomogeneous differential operator and an indefinite potential. In this paper we are concerned with two distinct cases. We first consider the case where the reaction is (

scholarly journals Compatibility conditions for nonlinear Neumann problems

1991 ◽  
Vol 89 (2) ◽  
pp. 127-143 ◽  
Author(s):  
Giuseppe Buttazzo ◽  
Franco Tomarelli
Keyword(s):  
Compatibility Conditions ◽  
Neumann Problems ◽  
Nonlinear Neumann Problems

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.

scholarly journals Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

2015 ◽  
Vol 145 (1) ◽  
pp. 31-45 ◽  
Author(s):  
Barbara Brandolini ◽  
Francesco Chiacchio ◽  
Cristina Trombetti
Keyword(s):  
Neumann Problems ◽  
Convexity Assumption ◽  
Planar Domains ◽  
Isoperimetric Constant ◽  
Linear And Nonlinear ◽  
Neumann Eigenvalue ◽  
The One ◽  
Nonlinear Neumann Problems ◽  
Sharp Lower Bound ◽  
Better Than

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.

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