Results 71 to 80 of about 59,795 (219)
Abstract and Applied Analysis, 2012 The second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert space H with the self-adjoint positive definite operator A.
Allaberen Ashyralyev, Ozgur Yildirim
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Linear ODE with nonlocal boundary conditions and Green’s functions for such problems
Lietuvos Matematikos Rinkinys, 2019 In this article we investigate a formula for the Green’s function for the n-order linear differential equation with n additional conditions. We use this formula for calculating the Green’s function for problems with nonlocal boundary conditions.
Svetlana Roman, Artūras Štikonas
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On a class of parabolic equations with nonlocal boundary conditions
Journal of Mathematical Analysis and Applications, 2004 The author considers the problem \[ \begin{aligned} &u_t = \nabla\cdot(d(x,t)\nabla u + \mathbf{W}(x,t)u), \quad (x,t)\in Q_T = \Omega\times(0,T],\\ &du_\nu + (\mathbf{W}\cdot\nu)u = \int_\Omega g(x,t,u)\,dx, \quad (x,t)\in S_T,\qquad u(x,0) = u_0(x), \quad x\in\Omega, \end{aligned} \] which is a generalized model for a theory of ion-diffusion in ...
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Nonlocal Integro-Differential Equations of the Second Order with Degeneration
Mathematics, 2020 We study the solvability for boundary value problems to some nonlocal second-order integro–differential equations that degenerate by a selected variable.
Aleksandr I. Kozhanov
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Study of Solutions to Some Functional Differential Equations with Piecewise Constant Arguments
Abstract and Applied Analysis, 2012 We provide optimal conditions for the existence and uniqueness of solutions to a nonlocal boundary value problem for a class of linear homogeneous second-order functional differential equations with piecewise constant arguments.
Juan J. Nieto, Rosana Rodríguez-López
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Nonlinear Analysis, 2014 In this paper, we present a survey of recent results on the Green's functions and on spectrum for stationary problems with nonlocal boundary conditions.
Artūras Štikonas
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On Nonlinear Parabolic Equations with Nonlocal Boundary Condition
Journal of Mathematical Analysis and Applications, 1994 Let \(\emptyset \neq \Omega \subset \mathbb{R}^ n\) be a bounded domain with \(C^ 2\)-boundary and \(T > 0\). Of concern is the semilinear second order initial-boundary value problem \[ \begin{alignedat}{2} \partial_ tu(t,x) - A(t)u(t,x) & = f \bigl( t,x,u(t,x) \bigr), &\qquad (t,x) &\in (0,T) \times \Omega, \\ u(t,x) & = \int_ \Omega \Phi (x,y) u(t,y)
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Solvability of the -Laplacian with nonlocal boundary conditions
Applied Mathematics and Computation, 2009 Rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form[@F(x^'(t))]^'+c(t)(Fx)(t)=0,[email protected]?(0,1),x(0)-L"0(x)=x(1)-L"1(x)=0,which unify several cases discussed in the literature. In order to formulate these conditions one needs to know only properties of the homeomorphism @
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Karpatsʹkì Matematičnì Publìkacìï, 2019 In this article we investigate a problem with nonlocal boundary conditions which are multipoint perturbations of mixed boundary conditions in the unit square $G$ using the Fourier method. The properties of a generalized transformation operator $R: L_2(G)
Ya.O. Baranetskij +3 more
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Diffusion with nonlocal Dirichlet boundary conditions on domains [PDF]
Studia Mathematica, 2020 We consider a second order differential operator $\mathscr{A}$ on an (typically unbounded) open and Dirichlet regular set $ \subset \mathbb{R}^d$ and subject to nonlocal Dirichlet boundary conditions of the form \[ u(z) = \int_ u(x) (z, dx) \quad \mbox{ for } z\in \partial .
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