scholarly journals Erratum to: ‘Abstract elliptic operators appearing in atmospheric dispersion’ by Veli B Shakhmurov and Aida Sahmurova published in the journal of Boundary Value Problems, 2014, V. 2014: 43

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Veli B Shakhmurov ◽  
Aida Sahmurova
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Atmospheric Dispersion ◽  
Elliptic Operators

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.

scholarly journals Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Vladimir Kozlov
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Operators ◽  
Elliptic Boundary Value Problems ◽  
Asymptotics Of Eigenvalues ◽  
Elliptic Boundary Value ◽  
Asymptotic Formulae ◽  
Variational Form ◽  
Leading Term

We consider eigenvalues of elliptic boundary value problems, written in variational form, when the leading coefficients are perturbed by terms which are small in some integral sense. We obtain asymptotic formulae. The main specific of these formulae is that the leading term is different from that in the corresponding formulae when the perturbation is small inL∞-norm.

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