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.

BIFURCATIONS FOR QUASILINEAR ELLIPTIC EQUATIONS, II

2008 ◽  
Vol 10 (05) ◽  
pp. 721-743 ◽  
Author(s):  
JIA-QUAN LIU ◽  
ZHI-QIANG WANG
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Structural Condition ◽  
Similar Type ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

This paper is concerned with bifurcation solutions of quasilinear elliptic problems. Our results generalize some earlier work, in particular, a similar type of result found in [3] where an additional structural condition is required to be imposed and the result in [11] where bifurcations in terms of the radius of the solutions were considered.

Soliton Solutions to a Class of Quasilinear Elliptic Equations on ℝ

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
M.J. Alves ◽  
P.C. Carrião ◽  
O.H. Miyagaki
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Soliton Solutions ◽  
Quasilinear Elliptic Equations ◽  
Concentration Compactness ◽  
Concentration Compactness Principle ◽  
Existence Of Positive Solutions ◽  
Compactness Principle ◽  
Quasilinear Elliptic ◽  
Minimization Approach

AbstractThis paper is concerned with the existence of positive solutions for a class of quasilinear elliptic equations on ℝ. The results are proved by combining the concentration-compactness principle due to Lions with a minimization approach.

QUASILINEAR ELLIPTIC EQUATIONS OF THE HENON-TYPE: EXISTENCE OF NON-RADIAL SOLUTIONS

2009 ◽  
Vol 11 (05) ◽  
pp. 783-798 ◽  
Author(s):  
P. C. CARRIÃO ◽  
D. G. DE FIGUEIREDO ◽  
O. H. MIYAGAKI
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Quasilinear Elliptic Equations ◽  
Open Ball ◽  
Radial Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

In this work, we prove results on existence and multiplicity of non-radial solutions for a class of singular quasilinear elliptic problems of the form [Formula: see text] where B = {x ∈ ℝN: |x| < 1} (N ≥ 3) is a unit open ball centered at the origin, -∞ < a < (N - p)/p, β > 0 and [Formula: see text].

scholarly journals Quasilinear Elliptic Equations with Hardy-Sobolev Critical Exponents: Existence and Multiplicity of Nontrivial Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guanwei Chen
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

scholarly journals Existence of positive solutions of quasilinear elliptic equations

1996 ◽  
Vol 54 (1) ◽  
pp. 147-154 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Exterior Domains ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

We prove under quite general assumptions the existence of a positive solution to the equation Δu + f(x, u) + g(x)x.∇u = 0 in exterior domains of Rn (n ≥ 3).

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