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Fractional boundary value problems with integral boundary conditions
Applicable Analysis, 2013In this article, we study a type of nonlinear fractional boundary value problem with integral boundary conditions. By constructing an associated Green's function, applying spectral theory and using fixed point theory on cones, we obtain criteria for the existence, multiplicity and nonexistence of positive solutions.
John R. Graef +3 more
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Boundary conditions for integrable discrete chains
Journal of Physics A: Mathematical and General, 2001It is known since the works of Birkhoff that (simple) recurrences (finite difference equations) of one integer index define a larger class of functions than the analogous ordinary differential equations (ODEs). Birkhoff has shown that the sequence of transformations from an integer index to a rational, and a fortiori to a continuous one is generally ...
Habibullin, I. T., Kazakova, T. G.
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Boundary conditions for integrable chains
Physics Letters A, 1995Abstract The quasi-periodicity and deeper reductions and boundary conditions compatible with the integrability property are discussed for the Volterra, the nonlinear Schrodinger and Toda lattices.
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Boundary conditions for integrable equations
Functional Analysis and Its Applications, 1987zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1994
We first consider an expository linear example: with conditions given as: γ, β 1,, and β 2 are assumed constants here although they can be functions of x with minor modifications to the procedure given. In decomposition format we have Lu + Ru = 0 or L−1Lu = I:−L−1 Ru or where is a two-fold pure integration with respect to x.
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We first consider an expository linear example: with conditions given as: γ, β 1,, and β 2 are assumed constants here although they can be functions of x with minor modifications to the procedure given. In decomposition format we have Lu + Ru = 0 or L−1Lu = I:−L−1 Ru or where is a two-fold pure integration with respect to x.
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Boundary Value Problems With Integral Conditions
AIP Conference Proceedings, 2011The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of
L. I. Karandzhulov +4 more
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On a boundary value problem with integral boundary conditions
Differential Equations, 2015We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions.
A. Ya. Lepin, L. A. Lepin
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Improved boundary integral method for inviscid boundary condition applications
AIAA Journal, 1993The potential part of an unsteady, incompressible, viscous flow is treated by means of a boundary integral method. Discretizing the surface of an object in form of panels, imposing inviscid boundary conditions (no flow through wall) and enforcing conservation of circulation leads to a problem which is not uniquely solvable but numerically ill-posed.
Koumoutsakos, P., Leonard, A.
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Integrable Boundary Conditions of the Modified Volterra Model
Journal of the Physical Society of Japan, 1997Summary: New boundary conditions of the so-called ``modified Volterra model'', which is described by a set of the nonlinear differential-difference equations, are presented. In accordance with the methods developed by Sklyanin, these conditions are shown to be integrable, including the simply truncated open-end case.
Kajinaga, Yasumasa, Wadati, Miki
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Integrable boundary conditions for many-component burgers equations
Mathematical Notes, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Svinolupov, S. I., Khabibullin, I. T.
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