Quasilinear Elliptic Equations on Half- and Quarter-spaces

2013 ◽  
Vol 13 (1) ◽  
Author(s):  
E.N. Dancer ◽  
Yihong Du ◽  
Messoud Efendiev
Keyword(s):  
Elliptic Equations ◽  
Type Theorem ◽  
Quasilinear Elliptic Equations ◽  
Positive Zero ◽  
One Dimensional ◽  
Quasilinear Elliptic Problems ◽  
The One ◽  
Quasilinear Elliptic ◽  
Special Case ◽  
Strong Comparison Principle

AbstractWe consider quasilinear elliptic problems of the form Δwhere V is a solution of the one-dimensional problemΔwith z a positive zero of f . Our results extend most of those in the recent paper of Efendiev and Hamel [6] for the special case p = 2 to the general case p > 1. Moreover, by making use of a sharper Liouville type theorem, some of the results in [6] are improved. To overcome the difficulty of the lack of a strong comparison principle for p-Laplacian problems, we employ a weak sweeping principle.

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.

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.

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 On the Harnack inequality for quasilinear elliptic equations with a first-order term

2018 ◽  
Vol 148 (5) ◽  
pp. 1075-1095 ◽  
Author(s):  
Susana Merchán ◽  
Luigi Montoro ◽  
Berardino Sciunzi
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Order Term ◽  
Quasilinear Elliptic Equations ◽  
First Order ◽  
Image Position ◽  
Quasilinear Elliptic ◽  
Comparison Inequality ◽  
Strong Comparison Principle ◽  
Iteration Technique

We consider weak solutions towith p > 1, q ≥ max{p − 1, 1}. We exploit the Moser iteration technique to prove a Harnack comparison inequality for C1 weak solutions. As a consequence we deduce a strong comparison principle.

scholarly journals On Carlson's Type Removability Test for the Degenerate Quasilinear Elliptic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
Farman I. Mamedov ◽  
Aslan D. Quliyev ◽  
Mirfaig M. Mirheydarli
Keyword(s):  
Hausdorff Measure ◽  
Elliptic Equations ◽  
Type Theorem ◽  
Quasilinear Elliptic Equations ◽  
Compact Set ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Muckenhoupt Class ◽  
Removable Sets ◽  
Quasilinear Elliptic

Carlson's type theorem on removable sets forα-Holder continuous solutions is investigated for the quasilinear elliptic equationsdiv A(x,u,∇u)=0,having degenerationωin the Muckenhoupt class. In partial, whenαis sufficiently small and the operator is weightedp-Laplacian, we show that the compact setEis removable if and only if the Hausdorff measureΛω−p+(p−1)α(E)=0.

Sign in / Sign up

Export Citation Format

Share Document