Multiplicity of periodic solutions for the planar polynomial equation

Borisovich, Andrei; Marzantowicz, Wacław

doi:10.1016/s0362-546x(99)00191-1

Cited by 8 publications

(10 citation statements)

References 11 publications

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“…The more general case of Floquet boundary conditions has been considered in [28,29,39]. The case of polynomial equations with coefficients belonging to the algebra of T-periodic functions with Fourier coefficients of negative index equal to zero has been recently initiated by Borisovich and Marzantowicz [3,4] and developed by Taddei [41].…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions of quaternionic-valued ordinary differential equations

Campos

Mawhin

2005

Annali di Matematica

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Section: Introductionmentioning

confidence: 99%

Periodic solutions of quaternionic-valued ordinary differential equations

Campos

Mawhin

2005

Annali di Matematica

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“…We will denote by C p + (T) the closure of subspace E(T) in C p (T) with respect to its norm · p . Definition 3.1 is equivalent to Definition 2.1, see [6]. We assign to a given period T > 0 the two dimensional open disc on the complex plane…”

Section: It Is Clear That E(t) Is a Subspace Of Every C P (T)mentioning

confidence: 99%

“…We will denote by C p + (T) the closure of subspace H(T) in C p (T) with respect to its norm · p . Definition 3.2 is equivalent to Definitions 2.1 and 3.1, see [6]. It is well known that the kernel subspace of multiplicative linear functional is a maximal ideal in the Banach algebra.…”

Section: T) We Call H(s τ ) or H(t) The Set Of Restrictions To The Bmentioning

confidence: 99%

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Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part

Borisovich

Marzantowicz

2006

Journal of Inequalities and Applications

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We study nonlinear ODE problems in the complex Euclidean space, with the right-hand side being polynomial with nonconstant periodic coefficients. As the coefficients functions, we admit only functions with vanishing Fourier coefficients for negative indices. This leads to an existence theorem which relates the number of solutions with the number of zeros of the averaged right-hand side polynomial. A priori estimates of the norms of solutions are based on the Wirtinger-Poincaré-type inequality. The proof of existence theorem is based on the continuation method of Krasnosielski et al., Mawhin et al., and the Leray-Schauder degree. We give a few applications on the complex Riccati equation and some others.

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“…[1,2,4,5,7,8,11,12,15]. One of the most important problems was to examine the structure of the set of periodic solutions.…”

Section: Introductionmentioning

confidence: 99%