Mirzov, J. D. On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems. (English) Zbl 0327.34027 J. Math. Anal. Appl. 53, 418-425 (1976). The author studies the following system of nonlinear differential equations \[ u_{1}^{\prime}=a_{1}(t)\left|u_{2}\right|^{\lambda_{1}} \operatorname{sign} u_{2}, \quad u_{2}^{\prime}=a_{2}(t)\left|u_{1}\right|^{\lambda_{2}} \operatorname{sign} u_{1} \] with \( \lambda_{i}>0, \lambda_{1} \lambda_{2}=1 \). He presents three theorems: A comparison result, an oscillatory and a non-oscillatory theorem. These theorems are generalizations of the corresponding results for linear second order equations. This review text is based on a scanned copy of the printed version. It was converted to LaTeX using MathPix and a specifically developed LLM to assign the text parts to the metadata. It may contain errors, misassignments, or gaps; in particular, the reviewer signature has not yet been extracted reliably in general. If you notice any errors, please report them directly to our editorial team via the Contact Form. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 69 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bellman, R., Stability Theory of Differential Equations, 1954, Izd. Inostr. Lit: Izd. Inostr. Lit Moscow, (in Russian) [2] Walter, W., Differential and Integral Inequalities, 1970, Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York · Zbl 0252.35005 [3] Izjumova, D. V., On the conditions of the oscillation and non-oscillation of solutions of a nonlinear second order differential equation, Differencial’nye Uravnenija, 2, 12, 1572-1586, 1966, (in Russian) · Zbl 0178.43901 [4] Mirzov, J. D., A remark on the oscillations of solutions of the system of ordinary differential equations, Soobšč. Akad. Nauk Gruzin. SSR, 61, 2, 277-279, 1971, (in Russian) · Zbl 0216.11402 [5] Mirzov, J. D., On the oscillations of solutions of the system of nonlinear differential equations, Differencial’nye Uravnenija, 9, 3, 581-583, 1973, (in Russian) · Zbl 0281.34028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.