scholarly journals Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents

2003 ◽  
Vol 20 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Elves A.B Silva ◽  
Magda S Xavier
Keyword(s):  
Elliptic Problems ◽  
Multiplicity Of Solutions ◽  
Critical Sobolev Exponents ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

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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