On the existence and concentration of positive solutions to a class of quasilinear elliptic problems on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}$\end{document}

2011 ◽  
Vol 284 (14-15) ◽  
pp. 1784-1795 ◽  
Author(s):  
Claudianor O. Alves ◽  
Olímpio H. Miyagaki ◽  
Sérgio H. Monari Soares
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

scholarly journals Positive solutions of critical quasilinear elliptic problems in general domains

1998 ◽  
Vol 3 (1-2) ◽  
pp. 65-84 ◽  
Author(s):  
Filippo Gazzola
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Critical Growth ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

Multiplicity Result for Quasilinear Elliptic Problems with General Growth in the Gradient

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Boumediene Abdellaoui
Keyword(s):  
Positive Solutions ◽  
Elliptic Problems ◽  
Multiplicity Result ◽  
General Growth ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe main result of this work is to get the existence of infinitely many radial positive solutions to the problem-Δwhere Ω = B

ON A CLASS OF QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL EXPONENTS

2000 ◽  
Vol 02 (01) ◽  
pp. 47-59 ◽  
Author(s):  
D. G. de FIGUEIREDO ◽  
J. V. GONÇALVES ◽  
O. H. MIYAGAKI
Keyword(s):  
Positive Solutions ◽  
Critical Exponents ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Real Numbers ◽  
Critical Sobolev Exponents ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

This paper deals with the following class of quasilinear elliptic problems in radial form [Formula: see text] where α, β, δ, ℓ, γ, q are given real numbers, λ > 0 is a parameter and 0 < R < ∞. Some results on the existence of positive solutions are obtained by combining the Mountain Pass Theorem with an argument used by Brézis and Nirenberg to overcome the lack of compactness due to the presence of critical Sobolev exponents.

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