Results 51 to 60 of about 551 (71)

Fractional differentiability for solutions of the inhomogenous $p$-Laplace system

, 2017
It is shown that if $p \ge 3$ and $u \in W^{1,p}(\Omega,\mathbb{R}^N)$ solves the inhomogenous $p$-Laplace system \[ \operatorname{div} (|\nabla u|^{p-2} \nabla u) = f, \qquad f \in W^{1,p'}(\Omega,\mathbb{R}^N), \] then locally the gradient $\nabla u ...
Miśkiewicz, Michał
core   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

An elliptic system with logarithmic nonlinearity

Advances in Nonlinear Analysis, 2017
In the present paper, we study the existence of solutions for some classes of singular systems involving the Δp⁢(x){\Delta_{p(x)}} and Δq⁢(x){\Delta_{q(x)}} Laplacian operators. The approach is based on bifurcation theory and the sub-supersolution method
Alves Claudianor, Moussaoui Abdelkrim, Tavares Leandro   +2 more
doaj   +1 more source

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

Advanced Nonlinear Studies, 2018
This paper is concerned with the following type of quasilinear elliptic equations in ℝN{\mathbb{R}^{N}} involving the p-Laplacian and critical growth:
Deng Yinbin, Peng Shuangjie, Wang Jixiu
doaj   +1 more source

Existence and regularity for a p-Laplacian problem in ℝN with singular, convective, and critical reaction

Advances in Nonlinear Analysis
We prove an existence result for a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction.
Baldelli Laura, Guarnotta Umberto
doaj   +1 more source

Quasilinear elliptic systems in divergence form associated to general nonlinearities

Advances in Nonlinear Analysis, 2018
The paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +1 more source

Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

Advanced Nonlinear Studies, 2020
We characterize the existence of solutions to the quasilinear Riccati-type ...
Nguyen Quoc-Hung, Phuc Nguyen Cong
doaj   +1 more source

Eigenvalues for Finsler p-Laplacian with zero Dirichlet boundary condition

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we analyze the problem - Qpu(x) = λu(x) when x∈Ω with u(x) = 0 when x∈Ω , where Ω⊂ℝN is a bounded domain, Qp stands for Finsler p-Laplacian and \ {2} is a given ...
Fărcăşeanu Maria
doaj   +1 more source

Sign-Changing Solutions of Fractional 𝑝-Laplacian Problems

Advanced Nonlinear Studies, 2019
In this paper, we obtain the existence and multiplicity of sign-changing solutions of the fractional p-Laplacian problems by applying the method of invariant sets of descending flow and minimax theory.
Chang Xiaojun, Nie Zhaohu, Wang Zhi-Qiang   +2 more
doaj   +1 more source