scholarly journals Existence and multiplicity of weak solutions for a singular semilinear elliptic equation

2008 ◽  
Vol 346 (1) ◽  
pp. 107-119 ◽  
Author(s):  
Zhou Wen-Shu
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Semilinear Elliptic Equation ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic

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 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 Multiple Positive Solutions for Semilinear Elliptic Equations in Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic Equations ◽  
Weight Functions ◽  
Multiple Positive Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation in , , where , if , if ), , satisfy suitable conditions, and may change sign in .

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