scholarly journals Weak solutions of semilinear elliptic equation involving Dirac mass

2018 ◽  
Vol 35 (3) ◽  
pp. 729-750 ◽  
Author(s):  
Huyuan Chen ◽  
Patricio Felmer ◽  
Jianfu Yang
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Semilinear Elliptic Equation ◽  
Dirac Mass ◽  
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.

Positive Solutions for Elliptic Equations With Supercritical Nonlinearity

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Paulo Rabelo
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Auxiliary Problem ◽  
Semilinear Elliptic Equation ◽  
Minimax Methods ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Supercritical Nonlinearity

AbstractIn this paper minimax methods are employed to establish the existence of a bounded positive solution for semilinear elliptic equation of the form−∆u + V (x)u = P(x)|u|where the nonlinearity has supercritical growth and the potential can change sign. The solutions of the problem above are obtained by proving a priori estimates for solutions of a suitable auxiliary problem.

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