Sultanaev, Y.T.; Valeev, N.F.; Nazirova, E.A. On the Asymptotic of Solutions of Odd-Order Two-Term Differential Equations. Mathematics2024, 12, 213.
Sultanaev, Y.T.; Valeev, N.F.; Nazirova, E.A. On the Asymptotic of Solutions of Odd-Order Two-Term Differential Equations. Mathematics 2024, 12, 213.
Sultanaev, Y.T.; Valeev, N.F.; Nazirova, E.A. On the Asymptotic of Solutions of Odd-Order Two-Term Differential Equations. Mathematics2024, 12, 213.
Sultanaev, Y.T.; Valeev, N.F.; Nazirova, E.A. On the Asymptotic of Solutions of Odd-Order Two-Term Differential Equations. Mathematics 2024, 12, 213.
Abstract
The work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.
Copyright:
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