Results 31 to 40 of about 1,637 (213)

The Brezis–Nirenberg problem for the fractional p-Laplacian [PDF]

Calculus of Variations and Partial Differential Equations, 2016
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional $p$-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when $p \ne 2$.
MOSCONI, SUNRA JOHANNES NIKOLAJ, Perera K, Squassina M, Yang Y.   +3 more
openaire   +5 more sources

Fractional p&q-Laplacian problems with potentials vanishing at infinity [PDF]

Opuscula Mathematica, 2020
In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional \(p\&q\)-Laplacian problems \[\begin{aligned} (-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(
Teresa Isernia
doaj   +1 more source

Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods

Advances in Mathematical Physics, 2017
We study the existence of nontrivial solution of the following equation without compactness: (-Δ)pαu+up-2u=f(x,u),  x∈RN, where N,p≥2,  α∈(0,1),  (-Δ)pα is the fractional p-Laplacian, and the subcritical p-superlinear term f∈C(RN×R) is 1-periodic in xi ...
Huxiao Luo, Shengjun Li, Xianhua Tang
doaj   +1 more source

Critical Fractional p-Laplacian System with Negative Exponents

Journal of Function Spaces, 2023
In this paper, we consider a class of fractional p-Laplacian problems with critical and negative exponents. By decomposition of the Nehari manifold, the existence and multiplicity of nontrivial solutions for the above problems are established with ...
Qinghao Zhu, Jianming Qi
doaj   +1 more source

Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian

Journal of Function Spaces and Applications, 2013
We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut ...
Ya-ling Li, Shi-you Lin
doaj   +1 more source

Lipschitz Regularity of Fractional p-Laplacian

Annals of PDE
31 pages, 1 ...
Biswas, Anup, Topp, Erwin
openaire   +2 more sources

Stability of variational eigenvalues for the fractional $p-$Laplacian [PDF]

Discrete and Continuous Dynamical Systems, 2015
35 pages.
BRASCO, Lorenzo, Parini, Enea, Squassina, Marco   +2 more
openaire   +3 more sources

A Hopf lemma and regularity for fractional $ p $-Laplacians

Discrete & Continuous Dynamical Systems - A, 2020
In this paper, we study qualitative properties of the fractional $p$-Laplacian. Specifically, we establish a Hopf type lemma for positive weak super-solutions of the fractional $p-$Laplacian equation with Dirichlet condition. Moreover, an optimal condition is obtained to ensure $(-\triangle)_p^s u\in C^1(\mathbb{R}^n)$ for smooth functions $u$.
Chen, Wenxiong, Li, Congming, Qi, Shijie
openaire   +4 more sources

On fractional p-Laplacian parabolic problem with general data [PDF]

Annali di Matematica Pura ed Applicata (1923 -), 2017
In this article the problem to be studied is the following $$ (P) \left\{ \begin{array}{rcll} u_t+(-\D^s_{p}) u & = & f(x,t) & \text{ in } _{T}\equiv \times (0,T), \\ u & = & 0 & \text{ in }(\ren\setminus ) \times (0,T), \\ u & \ge & 0 & \text{ in }\ren \times (0,T),\\ u(x,0) & = & u_0(x) & \mbox{ in
B. Abdellaoui, A. Attar, R. Bentifour, I. Peral   +3 more
openaire   +3 more sources

Fine boundary regularity for the degenerate fractional p-Laplacian

Journal of Functional Analysis, 2020
38 pages, 3 ...
Antonio Iannizzotto, Sunra Mosconi, Marco Squassina   +2 more
openaire   +2 more sources