Results 41 to 50 of about 569 (77)

Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes

, 2020
We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions.
Paoli, Gloria, Piscitelli, Gianpaolo, Trani, Leonardo   +2 more
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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
doaj   +1 more source

The Kellogg property and boundary regularity for p-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications

, 2018
In this paper boundary regularity for p-harmonic functions is studied with respect to the Mazurkiewicz boundary and other compactifications. In particular, the Kellogg property (which says that the set of irregular boundary points has capacity zero) is ...
Björn, Anders
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On the problem of unique continuation for the p-Laplace equation

, 2014
We study if two different solutions of the $p$-Laplace equation $$\nabla\cdot(|\nabla u|^{p-2}\nabla u)=0,$$ where ...
Alessandrini, Alessandrini, Bojarski, Del Pezzo, DiBenedetto, Evans, Garofalo, Garofalo, Gilbarg, Giusti, Heinonen, Juutinen, Král, Ladyzhenskaya, Lewis, Lewis, Manfredi, Niko Marola, Reshetnyak, Seppo Granlund, Tao, Tolksdorf   +21 more
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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

Positive solutions for nonvariational Robin problems

, 2018
We study a nonlinear Robin problem driven by the $p$-Laplacian and with a reaction term depending on the gradient (the convection term). Using the theory of nonlinear operators of monotone-type and the asymptotic analysis of a suitable perturbation of ...
Papageorgiou, Nikolaos S., Repovš, Dušan D., Rădulescu, Vicenţiu D.   +2 more
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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

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

Stability of eigenvalues for variable exponent problems

, 2015
In the framework of variable exponent Sobolev spaces, we prove that the variational eigenvalues defined by inf sup procedures of Rayleigh ratios for the Luxemburg norms are all stable under uniform convergence of the exponents.Comment: 10 ...
Colasuonno, Francesca, Squassina, Marco
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Normalized solutions for the double-phase problem with nonlocal reaction

Advances in Nonlinear Analysis
In this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
doaj   +1 more source