WEAK SOLUTIONS OF QUASILINEAR BIHARMONIC PROBLEMS WITH POSITIVE, INCREASING AND CONVEX NONLINEARITIES

2008 ◽  
Vol 06 (03) ◽  
pp. 213-227 ◽  
Author(s):  
I. ABID ◽  
M. JLELI ◽  
N. TRABELSI
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Weak Solutions ◽  
Source Term ◽  
Semilinear Elliptic Equation ◽  
Laplacian Operator ◽  
Navier Boundary Conditions ◽  
Semilinear Elliptic ◽  
Biharmonic Problems

We study the existence of positive weak solutions to a fourth-order semilinear elliptic equation with Navier boundary conditions and a positive, increasing and convex source term. We also prove the uniqueness of extremal solutions. In particular, we generalize results of Mironescu and Rădulescu for the bi-Laplacian operator.

scholarly journals A uniqueness result for some singular semilinear elliptic equations

2016 ◽  
Vol 18 (06) ◽  
pp. 1550084 ◽  
Author(s):  
Annamaria Canino ◽  
Berardino Sciunzi
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Open Subset ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Uniqueness Result ◽  
Dirichlet Boundary Conditions ◽  
Semilinear Elliptic ◽  
Bounded Open Subset

Given [Formula: see text] a bounded open subset of [Formula: see text], we consider non-negative solutions to the singular semilinear elliptic equation [Formula: see text] in [Formula: see text], under zero Dirichlet boundary conditions. For [Formula: see text] and [Formula: see text], we prove that the solution is unique.

scholarly journals Boundary singularities on a wedge-like domain of a semilinear elliptic equation

2015 ◽  
Vol 145 (5) ◽  
pp. 979-1006 ◽  
Author(s):  
Konstantinos T. Gkikas
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Semilinear Elliptic Equation ◽  
Fast Decay ◽  
Semilinear Elliptic ◽  
Image Position

Letn≥ 2 and letbe a Lipschitz wedge-like domain. We construct positive weak solutions of the problemthat vanish in a suitable trace sense on∂Ω, but which are singular at a prescribed ‘edge’ ofΩifpis equal to or slightly above a certain exponentp0> 1 that depends onΩ. Moreover, for the case in whichΩis unbounded, the solutions have fast decay at infinity.

scholarly journals On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem

2005 ◽  
Vol 2005 (6) ◽  
pp. 673-683
Author(s):  
Aixia Qian ◽  
Shujie Li
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Minimax Theory ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

By means of Minimax theory, we study the existence of one nontrivial solution and multiple nontrivial solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.

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