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On the stability of solutions of certain systems of differential equations with piecewise constant argument

Czechoslovak Mathematical Journal

We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.

On the difference equation ${x}_{n+1}=\frac{{a}_{0}{x}_{n}+{a}_{1}{x}_{n-1}+\cdots +{a}_{k}{x}_{n-k}}{{b}_{0}{x}_{n}+{b}_{1}{x}_{n-1}+\cdots +{b}_{k}{x}_{n-k}}$

Mathematica Bohemica

In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence ${x}_{n+1}=\frac{{a}_{0}{x}_{n}+{a}_{1}{x}_{n-1}+\cdots +{a}_{k}{x}_{n-k}}{{b}_{0}{x}_{n}+{b}_{1}{x}_{n-1}+\cdots +{b}_{k}{x}_{n-k}},\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}n=0,1,\cdots \phantom{\rule{0.166667em}{0ex}}\phantom{\rule{4pt}{0ex}}$ where the parameters ${a}_{i}$ and ${b}_{i}$ for $i=0,1,\cdots ,k$ are positive real numbers and the initial conditions ${x}_{-k},{x}_{-k+1},\cdots ,{x}_{0}$ are arbitrary positive numbers.

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