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Electronic Journal of Qualitative Theory of Differential Equations, 2019 We present general solutions to four classes of nonlinear difference equations, as well as some representations of the general solutions for two of the classes in terms of specially chosen solutions to linear homogeneous difference equations with ...
Stevo Stevic
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Note on a discrete initial value problem from a competition
Advances in Difference Equations, 2021 The following discrete initial value problem x n + 1 = x n ( x n − 1 2 − 2 ) − x 1 , n ∈ N , $$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, $$ x 0 = 2 $x_{0}=2$ and x 1 = 5 / 2 $x_{1}=5/2$ , appeared at an international ...
Stevo Stević
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Discrete supersymmetries of the Schrodinger equation and non-local exactly solvable potentials [PDF]
, 2003 Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term difference equation.
A.A Suzko +28 more
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Some representations of the general solution to a difference equation of additive type
Advances in Difference Equations, 2019 The general solution to the difference equation xn+1=axnxn−1xn−2+bxn−1xn−2+cxn−2+dxnxn−1xn−2,n∈N0, $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ where a,b,c∈C $a, b, c\in\mathbb{C}$, d∈
Stevo Stević
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Qualitative stability and solvability of difference equations [PDF]
Linear and Multilinear Algebra, 1991 We develop sufficient conditions for qualitative stability and solvability of the real discrete time system xt+ 1 = Axi + b. These conditions are a combination of qualitative and quantitative criteria and depend on signed digraphs.
Clark Jeffries, P. van den Driessche
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Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schr\"odinger Equations [PDF]
, 2009 On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schr\"odinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for ...
Quesne, Christiane
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Representations of general solutions to some classes of nonlinear difference equations
Advances in Difference Equations, 2019 Representations of general solutions to three related classes of nonlinear difference equations in terms of specially chosen solutions to linear difference equations with constant coefficients are given.
Stevo Stević +2 more
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Quantum cosmology of the brane universe [PDF]
, 2004 We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-deSitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial
Boyarsky, A., Neronov, A., Tkachev, I.
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Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension [PDF]
, 2016 We study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the
Bonini, Marisa +3 more
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Representation of solutions of a solvable nonlinear difference equation of second order
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic +3 more
doaj +1 more source