Abstract
The quasihomogeneous polynomials examined previously by the author, especially quasiquadratic forms [1, 2], are used to study some stability problems. The stability of systems of differential equations with quasihomogeneous right-hand sides is studied. Theorems analogous to the first-approximation Lyapunov stability theorems are derived for one class of essentially nonlinear systems of a special form. Several problems for these systems are examined that may be among the critical cases for these nonlinear systems of differential equations.
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REFERENCES
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Persidskii, S.K. Application of Quasihomogeneous Polynomials to Some Stability Problems. Journal of Mathematical Sciences 107, 4342–4346 (2001). https://doi.org/10.1023/A:1012583828942
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DOI: https://doi.org/10.1023/A:1012583828942