Sublinear Elliptic Equations With Singular Potentials

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Elliptic Equations ◽  
Singular Potentials ◽  
Marcinkiewicz Space ◽  
Solutions Of Equations

AbstractIn this paper we prove existence and summability results for solutions of equations whose model iswith a > 0 and f in some Marcinkiewicz space, thus extending the results of [4]. We the use these results to prove similar theorems for equations whose model iswith 0 < θ < 1 and p in some Marcinkiewicz space, thus extending the results of [3].

Some Remarks on Elliptic Equations with Singular Potentials and Mixed Boundary Conditions

2004 ◽  
Vol 4 (4) ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Eduardo Colorado ◽  
Ireneo Peral
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Singular Potentials

AbstractWe study the problemswhere

Liouville theorems for a class of fourth order elliptic equations

1980 ◽  
Vol 86 (1-2) ◽  
pp. 129-137 ◽  
Author(s):  
Vinod B. Goyal ◽  
Philip W. Schaefer
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Entire Solutions ◽  
Liouville Type ◽  
Liouville Theorems ◽  
Liouville Type Theorems ◽  
Solutions Of Equations ◽  
Fourth Order Elliptic Equations

SynopsisLiouville type theorems are obtained for bounded entire solutions of equations of the form Δ2u − q(x)Δu + p(x)u = 0 by means of subharmonic functionals and Green type inequalities.

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