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.

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.

scholarly journals Anisotropic 1-Laplacian problems with unbounded weights

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
Juan C. Ortiz Chata ◽  
Marcos T. O. Pimenta ◽  
Sergio Segura de León
Keyword(s):  
Bounded Variation ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Weighted Spaces ◽  
Laplacian Operator ◽  
Functions Of Bounded Variation ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractIn this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg’s inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting.

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

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