Results 41 to 50 of about 561 (74)

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
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Sharp Trudinger–Moser Inequality and Ground State Solutions to Quasi-Linear Schrödinger Equations with Degenerate Potentials in ℝn

Advanced Nonlinear Studies, 2021
The main purpose of this paper is to establish the existence of ground-state solutions to a class of Schrödinger equations with critical exponential growth involving the nonnegative, possibly degenerate, potential V:
Chen Lu, Lu Guozhen, Zhu Maochun
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A remark on an overdetermined problem in Riemannian Geometry

, 2015
Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$
A Enciso, A Farina, A Greco, A Greco, AL Vogel, Alberto Farina, B Brandolini, C Babaoglu, D Gilbarg, E Benedetto Di, E Hopf, GM Lieberman, HF Weinberger, J Heinonen, J Serrin, JL Lewis, M Choulli, N Garofalo, P Pucci, P Tolksdorf, QM Wang   +20 more
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Existence and multiplicity of solutions for a class of superlinear p-Laplacian equations

Advances in Nonlinear Analysis
In this work, we investigate a class of pp-Laplacian equations with the Dirichlet boundary condition. Under some new conditions, the existence and multiplicity of nontrivial solutions are proved by means of the variational methods.
Zhao Tai-Jin, Li Chun
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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
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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  

Existence of positive radial solutions of general quasilinear elliptic systems

Advances in Nonlinear Analysis
Let Ω⊂Rn(n≥2)\Omega \subset {{\mathbb{R}}}^{n}\hspace{0.33em}\left(n\ge 2) be either an open ball BR{B}_{R} centred at the origin or the whole space. We study the existence of positive, radial solutions of quasilinear elliptic systems of the form Δpu=f1(∣
Devine Daniel
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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
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Gradient estimates for a class of higher-order elliptic equations of p-growth over a nonsmooth domain

Advances in Nonlinear Analysis
This article is devoted to a global Calderón-Zygmund estimate in the framework of Lorentz spaces for the mm-order gradients of weak solution to a higher-order elliptic equation with pp-growth.
Tian Hong, Zheng Shenzhou
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Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions

Advanced Nonlinear Studies, 2018
In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have ...
Fernández Bonder Julian, Rossi Julio D., Spedaletti Juan F.   +2 more
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