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Real solutions of polynomial equations

Kiritsis K. H.

Control and Cybernetics

2017

Vol. 46, no. 2

177--185

In this paper the problem of existence of solution of polynomial equations over the ﬁeld of real numbers is considered. In particular, the explicit necessary and suﬃcient conditions are established for the equation A(z)X + B(z)Y = C(z) in polynomial matrices to have a solution for X and Y over the ﬁeld of real numbers, with X being non-singular, for every polynomial matrix C(z) from a given class.

Planar nonautonomous polynomial equations V. The Abel equation

Wilczyński P.

Opuscula Mathematica

2013

Vol. 33, no. 1

175-189

We give a full description of the dynamics of the Abel equation [formula] for some special complex valued ƒ. We also prove the existence of at least three periodic solutions for equations of the form [formula] for odd n ≥ 5.

Planar nonautonomous polynomial equations IV. Nonholomorphic case

Wilczyński P.

Opuscula Mathematica

2012

Vol. 32, no. 2

357-375

We give a few sufficient conditions for the existence of periodic solutions of the equation [formula] where n > r and aj 's, ck's are complex valued. We prove the existence of one up to two periodic solutions.

Solving polynomial equations

Jelonek Z.

Demonstratio Mathematica

2012

Vol. 45, nr 4

797-805

Let k be a field and (…) be a polynomial isomorphism. We give a formula for (…). In particular we show how to solve the equation (…).