Electron. J. Differential Equations, Vol. 2017 (2017), No. 261, pp. 1-9.

Trigonometric polynomial solutions of equivariant trigonometric polynomial Abel differential equations

Claudia Valls

Abstract:
Let $A(\theta)$ non-constant and $B_j(\theta)$ for $j=0,1,2,3$ be real trigonometric polynomials of degree at most $\eta \ge 1$ in the variable x. Then the real equivariant trigonometric polynomial Abel differential equations $A(\theta) y' =B_1(\theta) y +B_3 (\theta) y^3$ with $B_3 (\theta)\ne 0$, and the real polynomial equivariant trigonometric polynomial Abel differential equations of second kind $A(\theta) y y' = B_0(\theta)+ B_2(\theta) y^2$ with $B_2 (\theta)\ne 0$ 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.

Submitted August 27, 2017. Published October 16, 2017.
Math Subject Classifications: 34A05, 34C05, 37C10.
Key Words: Trigonometric polynomial Abel equations; equivariant trigonometric polynomial equation; trigonometric polynomial solutions

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Clàudia Valls
Departamento de Matemática
Instituto Superior Técnico
Universidade de Lisboa
Av. Rovisco Pais 1049--001, Lisboa, Portugal
email: cvalls@math.ist.utl.pt

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