Results 51 to 60 of about 1,480 (78)

Weyl-type laws for fractional p-eigenvalue problems

, 2014
We prove an asymptotic estimate for the growth of variational eigenvalues of fractional p-Laplacian eigenvalue problems on a smooth bounded domain.Comment: 10 ...
Iannizzotto, Antonio, Squassina, Marco
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Fractional Hardy-Sobolev equations with nonhomogeneous terms

Advances in Nonlinear Analysis, 2021
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity:
Bhakta Mousomi, Chakraborty Souptik, Pucci Patrizia   +2 more
doaj   +1 more source

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions [PDF]

, 2012
MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space ...
Al-Saqabi, Bader, Boyadjiev, Lyubomir
core  

General Fractional Calculus, Evolution Equations, and Renewal Processes

, 2011
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a nonnegative ...
Kochubei, Anatoly N.
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Existence and concentration of solutions for a fractional Schrödinger–Poisson system with discontinuous nonlinearity

Advanced Nonlinear Studies
In this paper, we study the following fractional Schrödinger–Poisson system with discontinuous nonlinearity:ε2s(−Δ)su+V(x)u+ϕu=H(u−β)f(u),inR3,ε2s(−Δ)sϕ=u2,inR3,u>0,inR3, $$\begin{cases}^{2s}{\left(-{\Delta}\right)}^{s}u+V\left(x\right)u+\phi u=H\left(u-\
Mu Changyang, Yang Zhipeng, Zhang Wei
doaj   +1 more source

Existence of Three Positive Solutions for a Nonlocal Singular Dirichlet Boundary Problem

Advanced Nonlinear Studies, 2019
In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem:
Giacomoni Jacques, Mukherjee Tuhina, Sreenadh Konijeti   +2 more
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Asymptotic behavior of extremals for fractional Sobolev inequalities associated with singular problems

, 2019
Let $\Omega$ be a smooth, bounded domain of $\mathbb{R}^{N}$, $\omega$ be a positive, $L^{1}$-normalized function, and ...
Ercole, Grey, Pereira, Gilberto Assis, Sanchis, Rémy   +2 more
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Fractional Perimeters from a Fractal Perspective

Advanced Nonlinear Studies, 2019
The purpose of this paper consists in a better understanding of the fractional nature of the nonlocal perimeters introduced in [L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces, Comm. Pure Appl. Math.
Lombardini Luca
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Critical fractional $p$-Laplacian problems with possibly vanishing potentials

, 2015
We obtain nontrivial solutions of a critical fractional $p$-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev ...
Perera, Kanishka, Squassina, Marco, Yang, Yang   +2 more
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Symmetrization for Mixed Operators

Annales Mathematicae Silesianae
In this paper, we prove Talenti's comparison theorem for mixed local/nonlocal elliptic operators and derive the Faber–Krahn inequality for the first eigenvalue of the Dirichlet mixed local/nonlocal problem. Our findings are relevant to the fractional p&q–
Bahrouni Sabri
doaj   +1 more source