Trigonometric polynomial solutions of equivariant trigonometric polynomial Abel differential equations
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Date
2017-10-16
Authors
Valls, Claudia
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let A(θ) non-constant and Bj(θ) for j = 0, 1, 2, 3 be real trigonometric polynomials of degree at most η ≥ 1 in the variable x. Then the real equivariant trigonometric polynomial Abel differential equations A(θ)y′ = B1(θ)y + B3(θ)y3 with B3(θ) ≠ 0, and the real polynomial equivariant trigonometric polynomial Abel differential equations of second kind A(θ)yy′ = B0(θ) + B2(θ)y2 with B2(θ) ≠ 0 have at most 7 real trigonometric polynomial solutions. Moreover there are real trigonometric polynomial equations of these type having these maximum number of trigonometric polynomial solutions.
Description
Keywords
Trigonometric polynomial Abel equations, Equivariant trigonometric polynomial equation, Trigonometric polynomial solutions
Citation
Valls, C. (2017). Trigonometric polynomial solutions of equivariant trigonometric polynomial Abel differential equations. <i>Electronic Journal of Differential Equations, 2017</i>(261), pp. 1-9.