Results 41 to 50 of about 533 (68)

Some remarks on sign changing solutions of a quasilinear elliptic equation in two variables [PDF]

, 2012
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative maximum and minimum values.
Granlund, Seppo, Marola, Niko
core  

Harnack inequality for a class of functionals with non-standard growth via De Giorgi’s method

Advances in Nonlinear Analysis, 2018
We study the regularity theory of quasi-minimizers of functionals with Lp⁢(⋅)⁢log⁡L{L^{p(\,\cdot\,)}\log L}-growth. In particular, we prove the Harnack inequality and, in addition, the local boundedness and the Hölder continuity of the quasi-minimizers ...
Ok Jihoon
doaj   +1 more source

On nonlinear potential theory, and regular boundary points, for the p-Laplacian in N space variables

Advances in Nonlinear Analysis, 2014
We turn back to some pioneering results concerning, in particular, nonlinear potential theory and non-homogeneous boundary value problems for the so-called p-Laplace operator.
Beirão da Veiga Hugo
doaj   +1 more source

A quasilinear problem with fast growing gradient

, 2012
In this paper we consider the following Dirichlet problem for the $p$-Laplacian in the positive parameters $\lambda$ and $\beta$: [{{array} [c]{rcll}% -\Delta_{p}u & = & \lambda h(x,u)+\beta f(x,u,\nabla u) & \text{in}\Omega u & = & 0 & \text{on}\partial\
Bueno, Hamilton, Ercole, Grey
core   +1 more source

The Nehari manifold for a quasilinear polyharmonic equation with exponential nonlinearities and a sign-changing weight function

Advances in Nonlinear Analysis, 2015
In this article, we consider the following quasilinear polyharmonic equation: Δn/mmu = λh(x)|u|q-1u + u|u|pe|u|β in Ω, u = ∇u = ⋯ = ∇m-1u = 0 on ∂Ω, where Ω ⊂ ℝn, n ≥ 2m ≥ 2, is a bounded domain with smooth boundary.
Goyal Sarika, Sreenadh Konijeti
doaj   +1 more source

On the existence and uniqueness of p-harmonious functions [PDF]

, 2012
We give a self-contained and short proof for the existence, uniqueness and measurability of so called $p$-harmonious functions. The proofs only use elementary analytic tools.
Luiro, Hannes, Parviainen, Mikko, Saksman, Eero   +2 more
core  

A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea

, 2012
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple cutoff.
Kreuzer, Christian
core   +1 more source

Existence and Multiplicity Results for a Class of Coupled Quasilinear Elliptic Systems of Gradient Type

Advanced Nonlinear Studies, 2021
The aim of this paper is investigating the existence of one or more weak solutions of the coupled quasilinear elliptic system of gradient ...
Candela Anna Maria, Salvatore Addolorata, Sportelli Caterina   +2 more
doaj   +1 more source

A note on the classification of positive solutions to the critical p-Laplace equation in Rn ${\mathbb{R}}^{n}$

Advanced Nonlinear Studies
In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in Rn ${\mathbb{R}}^{n}$ with n ≥ 4 and p > p n for some number pn∈n3,n+13 ${p}_{n}\in \left(\frac{n}{3},\frac{n+1}{3}\right)$ such that pn∼n3+1n $
Vétois Jérôme
doaj   +1 more source

On a Singular Robin Problem with Convection Terms

Advanced Nonlinear Studies, 2020
In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established.
Guarnotta Umberto, Marano Salvatore A., Motreanu Dumitru   +2 more
doaj   +1 more source