Results 31 to 40 of about 538 (68)
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. +2 more
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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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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
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Gradient and Lipschitz estimates for tug-of-war type games
, 2020 We define a random step size tug-of-war game, and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p ...
Attouchi, Amal +2 more
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Normalized solutions for the double-phase problem with nonlocal reaction
Advances in Nonlinear AnalysisIn 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
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Singular quasilinear elliptic systems in $\mathbb{R}^N$
, 2018 The existence of positive weak solutions to a singular quasilinear elliptic system in the whole space is established via suitable a priori estimates and Schauder's fixed point ...
Marano, S. A., Marino, G., Moussaoui, A.
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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(⋅)logL{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
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Existence results for double-phase problems via Morse theory
, 2016 We obtain nontrivial solutions for a class of double-phase problems using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups at zero.Comment: 11 ...
Perera, Kanishka, Squassina, Marco
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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
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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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