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].

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.

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.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

Existence of nodal solutions for quasilinear elliptic problems in ℝN

2015 ◽  
Vol 145 (5) ◽  
pp. 937-957
Author(s):  
Ann Derlet ◽  
François Genoud
Keyword(s):  
Elliptic Equations ◽  
Weighted Sobolev Space ◽  
Point Theory ◽  
Quasilinear Elliptic Equations ◽  
Nodal Solutions ◽  
Laplacian Equation ◽  
Quasilinear Elliptic Problems ◽  
Sign Changing Solutions ◽  
Quasilinear Elliptic ◽  
Constraint Minimization

We prove the existence of one positive, one negative and one sign-changing solution of a p-Laplacian equation on ℝN with a p-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on the whole of ℝN have scarcely been investigated in the literature. Our assumptions here are similar to those previously used by some authors in bounded domains, and our proof uses fairly elementary critical point theory, based on constraint minimization on the nodal Nehari set. The lack of compactness due to the unbounded domain is overcome by working in a suitable weighted Sobolev space.

scholarly journals Existence and multiplicity results for quasilinear elliptic equations

2005 ◽  
Vol 71 (3) ◽  
pp. 377-386 ◽  
Author(s):  
Wei Dong
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Bounded Open Subset ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic ◽  
Laplacian Operators

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

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