Results 11 to 20 of about 439 (53)
On an abstract nonlinear second order integrodifferential equation
Journal of Function Spaces, Volume 5, Issue 2, Page 167-174, 2007., 2007 The aim of the present paper is to study the global existence of solutions of nonlinear second order integrodifferential equation in Banach space. Our analysis is based on an application of the Leray‐Schauder alternative and rely on a priori bounds of solutions.
M. B. Dhakne, G. B. Lamb, Nigel Kalton
wiley +1 more source
The trajectory‐coherent approximation and the system of moments for the Hartree type equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 6, Page 325-370, 2002., 2002 The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB‐Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ → 0), are constructed with a power accuracy of O(ℏ N/2), where N is any natural number.
V. V. Belov +2 more
wiley +1 more source
Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds [PDF]
, 2010 By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise.
Wang, Feng-Yu
core +1 more source
Nonlocal elliptic equations in bounded domains: a survey [PDF]
, 2015 In this paper we survey some results on the Dirichlet problem \[\left\{ \begin{array}{rcll} L u &=&f&\textrm{in }\Omega \\ u&=&g&\textrm{in }\mathbb R^n\backslash\Omega \end{array}\right.\] for nonlocal operators of the form \[Lu(x)=\textrm{PV}\int_ ...
Ros-Oton, Xavier
core +4 more sources
Multiple solutions of nonlinear equations involving the square root of the Laplacian
, 2017 In this paper we examine the existence of multiple solutions of parametric fractional equations involving the square root of the Laplacian $A_{1/2}$ in a smooth bounded domain $\Omega\subset \mathbb{R}^n$ ($n\geq 2$) and with Dirichlet zero-boundary ...
Bisci, Giovanni Molica +2 more
core +5 more sources
Integro-differential systems with variable exponents of nonlinearity
Open Mathematics, 2017 Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
Buhrii Oleh, Buhrii Nataliya
doaj +1 more source
Advances in Nonlinear Analysis, 2019 This paper concerns the existence and multiplicity of solutions for the Schrődinger–Kirchhoff type problems involving the fractional p–Laplacian and critical exponent.
Xiang Mingqi +2 more
doaj +1 more source
Singular measure as principal eigenfunction of some nonlocal operators
, 2013 In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution $(\lambda,\phi)$ of a nonlocal operator. $$\int_{\O}K(x,y)\phi(y)
Coville, Jerome
core +1 more source
Transference of fractional Laplacian regularity
, 2014 In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus $\mathbb{T}^n$ from the fractional Laplacian on $\mathbb{R}^n$.
J.E. Galé +4 more
core +1 more source
Global Heat Kernel Estimates for Fractional Laplacians in Unbounded Open Sets [PDF]
, 2009 In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two classes of unbounded C^{1,1} open sets in R^d: half-space-like open sets ...
Chen, Zhen-Qing, Tokle, Joshua
core +3 more sources