A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations

1982 ◽  
pp. 133-155 ◽  
Author(s):  
D. G. De Figueiredo ◽  
P. L. Lions ◽  
R. D. Nussbaum
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Existence Of Positive Solutions

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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