On the diversity of Poincaré mappings for cubic equations with variable coefficients

DOI10.1007/BF02467118zbMath0955.34010MaRDI QIDQ1566489

A. A. Panov

Publication date: 12 February 2001

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Poincaré mapcyclic solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25)

Related Items (12)

Centennial History of Hilbert's 16th Problem ⋮ LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS ⋮ Periodic orbits in complex Abel equations ⋮ A new uniqueness criterion for the number of periodic orbits of Abel equations ⋮ A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ Chini equations and isochronous centers in three-dimensional differential systems ⋮ Periodic solutions for equation \(\dot x = A(t)x^m + B(t)x^n + C(t)x^l\) with \(A(t)\) and \(B(t)\) changing signs ⋮ ON POLYNOMIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER ON A CIRCLE WITHOUT SINGULAR POINTS ⋮ Periodic orbits for perturbed non-autonomous differential equations ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions ⋮ Planar nonautonomous polynomial equations II. Coinciding sectors

Cites Work

• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)

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