A priori estimates for a semilinear elliptic system without variational structure and their applications

2002 ◽  
Vol 323 (4) ◽  
pp. 713-735 ◽  
Author(s):  
Henghui Zou
Keyword(s):  
Elliptic System ◽  
A Priori Estimates ◽  
A Priori ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Semilinear Elliptic System ◽  
Variational Structure

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.

scholarly journals Singular quasilinear convective elliptic systems in ℝ N

2022 ◽  
Vol 11 (1) ◽  
pp. 741-756
Author(s):  
Umberto Guarnotta ◽  
Salvatore Angelo Marano ◽  
Abdelkrim Moussaoui
Keyword(s):  
Fixed Point ◽  
Weak Solution ◽  
Elliptic System ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Perturbation Techniques ◽  
Priori Estimates ◽  
Regularity Results

Abstract The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity results are then employed to show that the obtained solution is actually strong.

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