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957
Singular problems on the half–line∗
"... The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half–line of the form (p(t)u′(t)) ′ = p(t)f(u(t)), u′(0) = 0, u(∞) = L. The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved b ..."
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The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half–line of the form (p(t)u′(t)) ′ = p(t)f(u(t)), u′(0) = 0, u(∞) = L. The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved
Resonances in One Dimension and Fredholm Determinants
, 2000
"... We discuss resonances for Schrödinger operators in whole and halfline problems. One of our goals is to connect the Fredholm determinant approach of Froese to the Fourier transform approach of Zworski. Another is to prove a result on the number of antibound states namely, in a halfline problem the ..."
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Cited by 49 (1 self)
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We discuss resonances for Schrödinger operators in whole and halfline problems. One of our goals is to connect the Fredholm determinant approach of Froese to the Fourier transform approach of Zworski. Another is to prove a result on the number of antibound states namely, in a halfline problem
THE DEGASPERISPROCESI EQUATION ON THE HALFLINE
"... Abstract. We analyze a class of initialboundary value problems for the DegasperisProcesi equation on the halfline. Assuming that the solution u(x, t) exists, we show that it can be recovered from its initial and boundary values via the solution of a RiemannHilbert problem formulated in the plane ..."
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Cited by 1 (0 self)
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Abstract. We analyze a class of initialboundary value problems for the DegasperisProcesi equation on the halfline. Assuming that the solution u(x, t) exists, we show that it can be recovered from its initial and boundary values via the solution of a RiemannHilbert problem formulated
The Nonlinear Schrödinger equation on the halfline
 J. Math. Phys
, 1999
"... The nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structur ..."
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Cited by 3 (1 self)
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The nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic
SPECTRAL PROPERTIES OF THE CAUCHY PROCESS ON HALFLINE AND INTERVAL
, 2009
"... We study the spectral properties of the transition semigroup of the killed onedimensional Cauchy process on the halfline (0, ∞) and the interval (−1, 1). This process is related to the square root of onedimensional Laplacian A = − − d2 dx2 with a Dirichlet exterior condition (on a complement o ..."
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Cited by 10 (3 self)
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of a domain), and to a mixed Steklov problem in the halfplane. For the halfline, an explicit formula for generalized eigenfunctions ψλ of A is derived, and then used to construct spectral representation of A. Explicit formulas for the transition density of the killed Cauchy process in the halfline
The derivative nonlinear Schrödinger equation on the halfline
 Physica D
"... We analyze the derivative nonlinear Schrödinger equation iqt + qxx = i ( q  2q) x on the halfline using the Fokas method. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix RiemannHilbert problem formulated in the plane of the compl ..."
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Cited by 8 (3 self)
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We analyze the derivative nonlinear Schrödinger equation iqt + qxx = i ( q  2q) x on the halfline using the Fokas method. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix RiemannHilbert problem formulated in the plane
The KdV equation on a halfline
, 1999
"... Abstract. The initial boundary value problem on a halfline for the KdV equation with the boundary conditions ux=0 = a ≤ 0, uxxx=0 = 3a2 is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering matrix it turned out to be sufficient to solve the ..."
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Abstract. The initial boundary value problem on a halfline for the KdV equation with the boundary conditions ux=0 = a ≤ 0, uxxx=0 = 3a2 is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering matrix it turned out to be sufficient to solve
An integrable generalization of the sineGordon equation on the halfline
"... We analyze a generalization of the sineGordon equation in laboratory coordinates on the halfline. Using the Fokas transform method for the analysis of initialboundary value problems for integrable PDEs, we show that the solution u(x, t) can be constructed from the initial and boundary values via ..."
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We analyze a generalization of the sineGordon equation in laboratory coordinates on the halfline. Using the Fokas transform method for the analysis of initialboundary value problems for integrable PDEs, we show that the solution u(x, t) can be constructed from the initial and boundary values via
Positive Solutions of Operator Equations on HalfLine
"... In this paper, under the weaker conditions, we investigate the problem of the existence of positive solutions for operator equations on halfline. We establish some results on the existence of multiple positive solutions for operator equations on halfline by applying the fixedpoint theorem in a s ..."
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In this paper, under the weaker conditions, we investigate the problem of the existence of positive solutions for operator equations on halfline. We establish some results on the existence of multiple positive solutions for operator equations on halfline by applying the fixedpoint theorem in a
Evolution PDEs and augmented eigenfunctions. II halfline
, 2014
"... The solution of an initialboundary value problem for a linear evolution partial differential equation posed on the halfline can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90’s. On the o ..."
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The solution of an initialboundary value problem for a linear evolution partial differential equation posed on the halfline can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90’s
Results 1  10
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957