Results 101 to 110 of about 101,180 (174)
Principal eigenvalue of the fractional Laplacian with a large incompressible drift [PDF]
arXiv, 2013 We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and only if the drift has non-trivial first integrals in the domain of the quadratic form of the fractional Laplacian.
arxiv
Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$
Electronic Journal of Qualitative Theory of Differential EquationsIn the present paper, we study the nonexistence of nontrivial weak solutions to a class of fractional $p$-Laplacian equation in two cases which are $sp > N$ and $sp < N$.
Yuxin Chen, Haidong Liu
doaj +1 more source
Infinitely many non-radial sign-changing solutions for a Fractional Laplacian equation with critical nonlinearity [PDF]
arXiv, 2014 In this work, the following fractional Laplacian problem with pure critical nonlinearity is considered \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^{s} u=|u|^{\frac{4s}{N-2s}}u, &\mbox{in}\ \mathbb{R}^N, \\ u\in \mathcal{D}^{s,2}(\mathbb{R}^N), \end{array} \right. \end{equation*} where $s\in (0,1)$, $N$ is a positive integer with $N\geq 3$, $(-
arxiv
Abstract and Applied Analysis, 2014 We are concerned with the uniqueness of solutions for a class of p-Laplacian fractional order nonlinear systems with nonlocal boundary conditions.
Jun-qi He, Xue-li Song
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Further study on periodic solutions of elliptic equations with a fractional Laplacian [PDF]
arXiv, 2017 We obtain some existence theorems for periodic solutions to several linear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not larger than some exact positive constant.
arxiv
On Shape Optimization Theory With Fractional p-Laplacian Operators
Abstract and Applied AnalysisThe focus of this paper is the investigation of shape optimization problems with operators such as fractional Laplacian and p-Laplacian operators, that is, −Δs and −Δps, where ...
Malick Fall +3 more
doaj +1 more source
Singular critical elliptic problems with fractional Laplacian
Electronic Journal of Differential Equations, 2015 In this article, we consider the existence of solutions of the critical problem with a Hardy term for fractional Laplacian $$\displaylines{ (-\Delta)^s u -\mu \frac u{|x|^{2s}}= u^{2^*_s-1} \quad \text{in }\Omega,\cr u>0 \quad \text{in }\Omega, \cr
Xueqiao Wang, Jianfu Yang
doaj
A finite-volume scheme for fractional diffusion on bounded domains
European Journal of Applied MathematicsWe propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions.
Rafael Bailo +3 more
doaj +1 more source
Point-like perturbed fractional Laplacians through shrinking potentials of finite range [PDF]
arXiv, 2018 We reconstruct the rank-one, singular (point-like) perturbations of the $d$-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr\"{o}dinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape.
arxiv
Some functional inequalities for the fractional p-sub-Laplacian [PDF]
arXiv, 2018 In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on homogeneous Lie groups. We prove fractional Sobolev and Hardy inequalities and we also present a Lyapunov-type inequality for the fractional p-sub-Laplacian. As a consequence of the Lyapunov-type inequality we show an estimate of the first eigenvalue in a quasi ...
arxiv