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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Comparison results and steady states for the Fujita equation with fractional Laplacian
, 2003 Matthias Birkner +2 more
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The Neumann condition for the superposition of fractional Laplacians
ESAIM: Control, Optimisation and Calculus of VariationsWe present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties, existence and uniqueness results, asymptotic formulas, spectral analyses, rigidity results, integration by parts ...
Serena Dipierro +3 more
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Existence Results for $\aleph$-Caputo Fractional Boundary Value Problems with $p$-Laplacian Operator
Journal of New TheoryThis study delves into the investigation of positive solutions for a specific class of $\aleph$-Caputo fractional boundary value problems with the inclusion of the p-Laplacian operator. In this research, we use the theory of the fixed point theory within
Özlem Batit Özen
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Comparison results and steady states for the Fujita equation with fractional Laplacian
, 2004 José Alfredo López-Mimbela +2 more
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Momentum transforms and Laplacians in fractional spaces [PDF]
, 2012 Gianluca Calcagni, Giuseppe Nardelli
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Global solution for wave equation involving the fractional Laplacian with logarithmic nonlinearity
Electronic Research ArchiveWe construct the global existence for a wave equation involving the fractional Laplacian with a logarithmic nonlinear source by using the Galerkin approximations.
Bidi Younes +4 more
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Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian. [PDF]
J Inequal Appl, 2018 Qu M, Yang L.
europepmc +1 more source
Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian
, 2005 Krzysztof Bogdan, Paweł Sztonyk
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