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Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations

N. Parhi (2011)

Mathematica Bohemica

In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form Δ ( p n - 1 Δ y n - 1 ) + q y n = 0 , n ≥ 1 , where q is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type Δ ( p n - 1 Δ y n - 1 ) + q n g ( y n ) = f n - 1 , n ≥ 1 , where, unlike earlier works, f n ≥ 0 or ≤ 0 (but ¬ ≡ 0 ) for large n . Further, these results are used to obtain...

Nonuniqueness of implicit lattice Nagumo equation

Petr Stehlík, Jonáš Volek (2019)

Applications of Mathematics

We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness...

Note on a discretization of a linear fractional differential equation

Jan Čermák, Tomáš Kisela (2010)

Mathematica Bohemica

The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

Note on simultaneous solutions of a system of Schröder's equations

Jan Čermák (1995)

Mathematica Bohemica

We investigate simultaneous solutions of a system of Schroder's functional equations. Under certain assumptions these solutions are used in transformations of functional-differential equations the initial set of which consists of the initial point only.

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