scholarly journals Behaviour of solutions to the dirichlet problem for the biharmonic operator at a boundary point

1979 ◽  
pp. 250-262 ◽  
Author(s):  
V. G. Maz'ya
Keyword(s):  
Dirichlet Problem ◽  
Boundary Point ◽  
Biharmonic Operator

scholarly journals Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

2020 ◽  
Vol 6 (2) ◽  
pp. 198-209
Author(s):  
Mohamed Laghzal ◽  
Abdelouahed El Khalil ◽  
My Driss Morchid Alaoui ◽  
Abdelfattah Touzani
Keyword(s):  
Dirichlet Problem ◽  
Variational Approach ◽  
Type Inequality ◽  
Biharmonic Operator ◽  
Nondecreasing Sequence ◽  
Hardy Type Inequality ◽  
Principal Curve ◽  
Hardy Type ◽  
Homogeneous Dirichlet Problem

AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point

2020 ◽  
Vol 31 (2) ◽  
pp. 251-271 ◽  
Author(s):  
Yu. A. Alkhutov ◽  
M. D. Surnachev
Keyword(s):  
Dirichlet Problem ◽  
Boundary Point
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