Results 1 to 10 of about 528,042 (304)
Spike solutions to a nonlocal differential equation
Communications on Pure & Applied Analysis, 2006 In this paper we consider a nonlocal differential equation, which is a limiting equation of one dimensional Gierer-Meinhardt model. We study the existence of spike steady states and their stability. We also construct a single-spike quasi-equilibrium solution and investigate the dynamics of spike-like solutions.
Changfeng Gui, Zhenbu Zhang
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On a nonlocal differential equation describing roots of polynomials under differentiation [PDF]
Communications in Mathematical Sciences, 2018 In this work we study the nonlocal transport equation derived recently by Steinerberger when studying how the distribution of roots of a polynomial behaves under iterated differentation of the function.
Rafael Granero-Belinch'on
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Functional differential equations with nonlocal initial conditions [PDF]
International Journal of Stochastic Analysis, 1996 We study the existence, uniqueness, asymptotic properties, and continuous dependence upon data of solutions to a class of abstract nonlocal Cauchy problems. The approach we use is based on the theory of m‐accretive operators and related evolution equations in Banach spaces.
Sergiu Aizicovici, Yun Gao
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Symmetries and reductions of integrable nonlocal partial differential equations [PDF]
Symmetry, 2019 In this paper, symmetry analysis is extended to study nonlocal differential equations, in particular two integrable nonlocal equations, the nonlocal nonlinear Schr\"odinger equation and the nonlocal modified Korteweg--de Vries equation.
Peng, Linyu
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Existence theorems for a class of nonlocal differential equations
Journal of Mathematical Analysis and Applications, 2005 AbstractA class of nonlocal second-order ordinary differential equations of the formy″(x)=f(x,y(x),(y○λ)(x),y′(x)) for continuous f and λ is studied. The equation is supplemented with none, one, or two Robin boundary conditions depending on whether the interval of interest I is finite, semi-infinite or infinite.
Ronald Begg
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Existence of Solutions of Nonlinear Differential Equations with Nonlocal Conditions
Journal of Mathematical Analysis and Applications, 2000 The authors consider the initial value problem for an abstract nonlinear ordinary differential equation of first order in some Banach space. The initial condition, which is a nonlocal condition, is of the type \(y(0)+ g(y)=y_0\), where \(g\) is some continuous function.
Mouffak Benchohra, Sotiris K. Ntouyas
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Mild Solutions for Fractional Differential Equations with Nonlocal Conditions [PDF]
Advances in Difference Equations, 2010 This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions , in a Banach space , where . General existence and uniqueness theorem, which extends many previous results, are given.
Fang Li
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Large time behavior and Lyapunov functionals for a nonlocal differential equation [PDF]
, 2015 A new approach is used to describe the large time behavior of the nonlocal differential equation initially studied in T.-N. Nguyen (On the $${\omega}$$ω-limit set of a nonlocal differential equation: application of rearrangement theory. Differ.
Danielle Hilhorst +2 more
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Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation [PDF]
, 2016 We obtain Schauder estimates for a general class of linear integro-differential equations. The estimates are applied to a scalar non-local Burgers equation and complete the global well-posedness results obtained in \cite{ISV}.
Cyril Imbert +2 more
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Nonlocal diffusion second order partial differential equations
Journal of Differential Equations, 2016 Abstract The paper deals with a second order integro-partial differential equation in R n with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied.
Irene Benedetti +3 more
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