scholarly journals A nonlinear boundary problem involving thep-bilaplacian operator

2005 ◽  
Vol 2005 (10) ◽  
pp. 1525-1537 ◽  
Author(s):  
Abdelouahed El Khalil ◽  
Siham Kellati ◽  
Abdelfattah Touzani
Keyword(s):  
Boundary Conditions ◽  
Boundary Problem ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nondecreasing Sequence ◽  
Nonlinear Boundary Problem

We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditionsΔp2u+|u|p−2u=0inΩand−(∂/∂n)(|Δu|p−2Δu)=λρ|u|p−2uon∂Ωpossess at least one nondecreasing sequence of positive eigenvalues.

scholarly journals Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects

2019 ◽  
pp. 335-348
Author(s):  
Cristiane Aparecida Pendeza Martinez ◽  
André Luís Machado Martinez ◽  
Glaucia Maria Bressan ◽  
Emerson Vitor Castelani ◽  
Roberto Molina de Souza
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Fourth Order Equation

scholarly journals Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Quang A. Dang ◽  
Nguyen Thanh Huong
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Beam Equation ◽  
Linear Boundary ◽  
Order Problem ◽  
Fourth Order Problem

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.

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