Yang–Li's conjecture on meromorphic solutions of a polynomial differential equation

About 1 year old · traced to

Let P1P_1, P2P_2 and P3P_3 be non-zero polynomials. Consider the differential equation

P1f2+P2(f(1))2=P3.P_1f^2+P_2(f^{(1)})^2=P_3.

Yang–Li's conjecture. The equation has no transcendental meromorphic solution when P1/P3P_1/P_3 is a non-zero constant and P2/P3P_2/P_3 is not the square of any rational function.

This conjecture concerns the existence of transcendental meromorphic solutions for a first-order nonlinear differential equation with polynomial coefficients. The supplied text gives no evidence that the conjecture has been resolved.

References

Primary source

Sujoy majumder, Nabadwip Sarkar and Debabrata pramanik, “Meromorphic solutions of a certain type of nonlinear differential equation”, arXiv:2512.15750 (2025).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.