Linear Elliptic Operators and Variational Theory of Boundary Value Problems

2018 ◽  
pp. 141-172
Author(s):  
Michael Pedersen
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Operators ◽  
Variational Theory

Nonlinear Resonance: a Comparison Between Landesman-Lazer and Ahmad-Lazer-Paul Conditions

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Alessandro Fonda ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlinear Resonance ◽  
Elliptic Operators ◽  
Scalar Case ◽  
Asymmetric Oscillator ◽  
Existence Conditions

AbstractWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

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