Riccati differential equations with elliptic coefficients. II
The authors continue their study of solutions of the Riccati differential equation of form \(w' + w^2 +a\wp(z)=0\) [Result. Math. 38, 58--71 (2000; Zbl 0954.34076)]. They modify slightly the Weierstrass \(\wp\)-function and obtain results which are analogies to the previous. It gives us an idea, when \(m\) is an odd integer, there are no logarithmic singularities [\textit{N. V. Grigorenko}, Math. Notes 33, 453--454 (1983); translation from Mat. Zametki 33, No. 6, 881--884 (1983; Zbl 0549.34005) and Math. Notes 51, No. 6, 627 (1992); translation from Mat. Zametki 51, No. 6, 155 (1992; Zbl 0792.34005)] in solutions of the equation for any choice of the Weierstrass \(\wp\)-function. Moreover the associated operator \(y''+ +a\wp(z)y\) is algebro-geometric [\textit{R. Weikard}, Electron. J. Differ. Equ. 2000, Paper No. 19 (2000; Zbl 0953.34073)].
scientific article; zbMATH DE number 2040358