On Existence of Vanishing at Infinity Solutions to Second-Order Linear Differential Equations with Low-Degree Polynomial Coefficients

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Abstract: We study a second order linear differential equation with low-degree polynomial coefficients arising while studying the Bellman equation for the investment portfolio control problem. Our purpose is to determine whether there exists a non-trivial solution vanishing at infinity. We prove an existence criterion for such solutions according to the signs of the coefficients. By the way, the same methods produce an existence criterion for non-trivial bounded solutions. Instead of a verbose formulation, a united criterion is presented in a table form admitting simple computer realization.

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 13, 2018, Art. #44

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Alexander Astashov, Irina Astashova, Aleksey Shamaev, "On Existence of Vanishing at Infinity Solutions to Second-Order Linear Differential Equations with Low-Degree Polynomial Coefficients," WSEAS Transactions on Systems and Control, vol. 13, pp. 409-419, 2018, DOI:
Alexander Astashov, Irina Astashova, Aleksey Shamaev. On Existence of Vanishing at Infinity Solutions to Second-Order Linear Differential Equations with Low-Degree Polynomial Coefficients. WSEAS Transactions on Systems and Control. 2018;13:409-419.
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