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(EDP Sciences, 2014-10)A famous conjecture made by Lord Rayleigh is the following: “The first eigenvalue of the Laplacian on an open domain of given measure with Dirichlet boundary conditions is minimum when the domain is a ball and only when ...
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(AIP Publishing, 2015-03)or a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrödinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL, and ...
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(Elsevier B.V., 2019-05)We study the nonlocal scalar field equation with a vanishing parameter:(Pϵ){(−Δ)su+ϵu=|u|p−2u−|u|q−2uinRNu∈Hs(RN),where s∈(0,1), N>2s, q>p>2 are fixed parameters and ϵ>0 is a vanishing parameter. For ϵ small, we prove the ...
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(Springer Nature, 2023-03)The pair annihilation of neutrinos (nu(nu) over bar -> e(+)e(-)) can energize violent stellar explosions such as gamma ray bursts (GRBs). The energy in this neutrino heating mechanism can be further enhanced by modifying ...
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