Results 41 to 50 of about 96,434 (313)
A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations
Journal of Applied Mathematics, 2012 This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness
Fang Li +3 more
doaj +1 more source
Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity [PDF]
, 2010 We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero ...
André de Laire +15 more
core +3 more sources
Nonlocal isoperimetric problems
, 2014 We characterize the volume-constrained minimizers of a nonlocal free energy given by the difference of fractional perimeters. Exploiting the quantitative fractional isoperimetric inequality, we show that balls are the unique minimizers if the volume is sufficiently small, while the existence vs. nonexistence of minimizers for large volumes remains open.
Di Castro, Agnese +3 more
openaire +2 more sources
Doklady Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savin A.Yu., Sternin B.Yu.
openaire +4 more sources
Nonlocal problems with critical Hardy nonlinearity [PDF]
Journal of Functional Analysis, 2018 By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.
Chen, Wenjing +2 more
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Nonlinear Analysis, 2009 In this paper the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions is investigated numerically. The special cases of general problem are analyzed and hypothesis about the dependence of the spectral structure ...
S. Sajavičius, M. Sapagovas
doaj +1 more source
Discrete Dynamics in Nature and Society, 2009 The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The second-order of accuracy 𝑟-modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented ...
Allaberen Ashyralyev, Ali Sirma
doaj +1 more source
The fractional Cheeger problem
, 2013 Given an open and bounded set $\Omega\subset\mathbb{R}^N$, we consider the problem of minimizing the ratio between the $s-$perimeter and the $N-$dimensional Lebesgue measure among subsets of $\Omega$.
Brasco, Lorenzo +2 more
core +4 more sources
Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading
Advanced Engineering Materials, EarlyView.The approach by Amor and the approach by Miehe and Zhang for asymmetric damage behavior in the phase field method for fracture are compared regarding their fitness for microcrack‐based failure modeling. The comparison is performed for the case of a dual‐phase microstructure with a brittle and a ductile constituent.
Jakob Huber, Jan Torgersen, Ewald Werner
wiley +1 more source
Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity [PDF]
, 2009 We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is ...
Duruk, Nilay +3 more
core +1 more source