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.

Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

2006 ◽  
Vol 136 (6) ◽  
pp. 1131-1155 ◽  
Author(s):  
B. Amaziane ◽  
L. Pankratov ◽  
A. Piatnitski
Keyword(s):  
Elliptic Equation ◽  
Asymptotic Behaviour ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Equation ◽  
Quasilinear Elliptic Equations ◽  
High Contrast ◽  
Small Measure ◽  
Image Position ◽  
Quasilinear Elliptic

The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the form with a high-contrast discontinuous coefficient aε(x), where ε is the parameter characterizing the scale of the microstucture. The coefficient aε(x) is assumed to degenerate everywhere in the domain Ω except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution uε as ε → 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain Ω.

scholarly journals EXISTENCE OF POSITIVE EVANESCENT SOLUTIONS TO SOME QUASILINEAR ELLIPTIC EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 157-162 ◽  
Author(s):  
OCTAVIAN G. MUSTAFA
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Exterior Domain ◽  
Quasilinear Elliptic Equations ◽  
Image Position ◽  
Quasilinear Elliptic

AbstractWe establish that the elliptic equation defined in an exterior domain of ℝn, n≥3, has a positive solution which decays to 0 as $\vert x\vert \rightarrow +\infty $ under quite general assumptions upon f and g.

Nodal Solutions for a Quasilinear Elliptic Equation Involving the p-Laplacian and Critical Exponents

2018 ◽  
Vol 18 (1) ◽  
pp. 17-40
Author(s):  
Yinbin Deng ◽  
Shuangjie Peng ◽  
Jixiu Wang
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Quasilinear Elliptic Equations ◽  
Nodal Solution ◽  
Nodal Solutions ◽  
Content Type ◽  
Nodal Domains ◽  
Change Of Variables ◽  
Graphic Content ◽  
Quasilinear Elliptic

AbstractThis paper is concerned with the following type of quasilinear elliptic equations in{\mathbb{R}^{N}}involving thep-Laplacian and critical growth:-\Delta_{p}u+V(|x|)|u|^{p-2}u-\Delta_{p}(|u|^{2})u=\lambda|u|^{q-2}u+|u|^{2p^{% *}-2}u,which arises as a model in mathematical physics, where{2<p<N},{p^{*}=\frac{Np}{N-p}}. For any given integer{k\geq 0}, by using change of variables and minimization arguments, we obtain, under some additional assumptions onpandq, a radial sign-changing nodal solution with{k+1}nodal domains. Since the critical exponent appears and the lower order term (obtained by a transformation) may change sign, we shall use delicate arguments.

scholarly journals Uniqueness of weak solution for nonlinear elliptic equations in divergence form

2000 ◽  
Vol 23 (5) ◽  
pp. 313-318 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Divergence Form ◽  
Uniqueness Result ◽  
Quasilinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Quasilinear Elliptic

We study the uniqueness of weak solutions for quasilinear elliptic equations in divergence form. Some counterexamples are given to show that our uniqueness result cannot be improved in the general case.

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