Results 91 to 100 of about 416,411 (208)

Bifurcation and multiplicity of solutions for the fractional Laplacian with critical exponential nonlinearity

Electronic Journal of Differential Equations, 2016
We study the fractional elliptic equation $$\displaylines{ (-\Delta)^{1/2} u = \lambda u+|u|^{p-2}ue^{u^2} ,\quad\text{in } (-1,1),\cr u=0\quad\text{in } \mathbb{R}\setminus(-1,1), }$$ where $\lambda$ is a positive real parameter, p>2 and $(-\Delta)^
Pawan Kumar Mishra, Konijeti Sreenadh
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Null controllability from the exterior of fractional parabolic-elliptic coupled systems

Electronic Journal of Differential Equations, 2020
We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian $(-d_x^2)^s$, $s\in(0,1)$, in one space dimension.
Carole Louis-Rose
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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
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Pitt's inequality and the fractional Laplacian: Sharp error estimates [PDF]

, 2011
William Beckner
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New Results for p-Laplacian Fractional Instantaneous and Noninstantaneous Impulsive Differential Equations

Journal of Function Spaces
The p-Laplacian fractional differential equations have been studied extensively because of their numerous applications in science and engineering.
Wangjin Yao, Huiping Zhang
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Optimization problems in rearrangement classes for fractional $ p $-Laplacian equations

Mathematics in Engineering
We discuss two optimization problems related to the fractional $ p $-Laplacian. First, we prove the existence of at least one minimizer for the principal eigenvalue of the fractional $ p $-Laplacian with Dirichlet conditions, with a bounded weight ...
Antonio Iannizzotto, Giovanni Porru
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Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation [PDF]

, 2012
Zhen-Qing Chen, Panki Kim, Renming Song
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Comparison results and steady states for the Fujita equation with fractional Laplacian

, 2003
Matthias Birkner, José Alfredo López-Mimbela, Anton Wakolbinger   +2 more
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Asymmetric critical fractional p-Laplacian problems

Electronic Journal of Differential Equations, 2017
We consider the asymmetric critical fractional p-Laplacian problem $$\displaylines{ (-\Delta)^s_p u = \lambda |u|^{p-2} u + u^{p^\ast_s - 1}_+,\quad \text{in } \Omega;\cr u = 0, \quad \text{in } \mathbb{R}^N\setminus\Omega; }$$ where $\lambda>0 ...
Li Huang, Yang Yang
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Fractional stochastic heat equation with mixed operator and driven by fractional-type noise

AIMS Mathematics
We investigated a novel stochastic fractional partial differential equation (FPDE) characterized by a mixed operator that integrated the standard Laplacian, the fractional Laplacian, and the gradient operator.
Mounir Zili , Eya Zougar , Mohamed Rhaima   +2 more
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