A classification of the solutions of a differential equation according to their asymptotic behaviour

DOI10.1017/S0308210500011343zbMath0407.34042WikidataQ115335923 ScholiaQ115335923MaRDI QIDQ4193781

Uri Elias

Publication date: 1979

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

Asymptotic BehaviourLinear Differential EquationsClassification of the Solutions

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Qualitative theory for ordinary differential equations (34C99) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (15)

Structure of the solution space of certain linear equations ⋮ Oscillation results for Emden-Fowler type differential equations ⋮ A classification of the solutions of a difference equation according to their behavior at infinity ⋮ A classification of the solutions of a differential equation according to their behaviour at infinity, II ⋮ Growth properties of solutions to a linear differential equation ⋮ Green's function for a non-disconjugate differential operator ⋮ Minors of the wronskian of the differential equation L_ny+p(x)y=0 ⋮ Periodic solutions and invariant manifolds for an even-order differential equation with power nonlinearity ⋮ Equivalency for Disconjugate Operators ⋮ Properties of minors of the Wronskian for solutions of \(L_ ny+p(x)y=0\) as related to (k,n-k) disfocality ⋮ Minors of the Wronskian of the differential equation L_ny + p(x)y = 0. II. Dominance of solutions ⋮ On a cyclic disconjugate operator associated to linear differential equations ⋮ On nonlinear oscillations for equations associated to disconjugate operators ⋮ Extremal solutions for \(n\)th order linear difference equations ⋮ Integral criteria for a classification of solutions of linear differential equations

Cites Work

• Oscillation criteria for third-order linear differential equations
• Dominance of \(n\)-th order linear equations
• Oscillation properties of certain self-adjoint differential equations of the fourth order
• The essential uniqueness of bounded nonoscillatory solutions of certain even order differential equations
• Nonoscillatory solutions of a class of nth-order linear differential equations
• The behavior of solutions of the differential equation \(y+p(x)y'+q(x)y = 0\)
• On the oscillatory behavior of a class of linear third order differential equations
• Oscillatory and Asymptotic Characterization of the Solutions of Differential Equations with Deviating Arguments
• Linear Differential and Difference Equations with Monotone Solutions

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