Canonical Forms and Principal Systems for General Disconjugate Equations

DOI10.2307/1996862zbMath0289.34051OpenAlexW4239983067MaRDI QIDQ4777703

William F. Trench

Publication date: 1974

Full work available at URL: https://doi.org/10.2307/1996862

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Qualitative theory for ordinary differential equations (34C99)

Related Items (80)

On the behaviour of solutions to a kind of third order nonlinear neutral differential equation with delay ⋮ Bounds for solutions of multipoint boundary value problems ⋮ Nonoscillation and Eventual Disconjugacy ⋮ Sharp nonoscillation theorems for even-order elliptic equations ⋮ Oscillation and nonoscillation criteria for nth-order linear differential equations ⋮ On asymptotic behavior of delay-differential equations of third order ⋮ Asymptotic behavior of third-order functional differential equations with a negative middle term ⋮ Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms ⋮ Oscillation of noncanonical second-order functional differential equations via canonical transformation ⋮ Oscillation results for Emden-Fowler type differential equations ⋮ Unnamed Item ⋮ Polynomial asymptotic expansions in the real domain: the geometric, the factorizational, and the stabilization approaches ⋮ Oscillation criteria for forced functional differential equations with deviating arguments ⋮ Oscillation of second-order half-linear retarded difference equations via a canonical transform ⋮ A note on oscillation of second-order delay differential equations ⋮ Oscillatory behavior of the second order noncanonical differential equations ⋮ Oscillation criteria of Kneser-type for second-order half-linear advanced differential equations ⋮ Oscillation of fourth-order strongly noncanonical differential equations with delay argument ⋮ Nonlinear oscillation of a fourth order elliptic equation ⋮ Asymptotic integration of higher order nonlinear delay differential equations via principal solutions ⋮ Green's function for a non-disconjugate differential operator ⋮ The fourth order strongly noncanonical operators ⋮ Unbounded positive entire solutions of semilinear elliptic equations ⋮ Oscillatory behavior of semi-canonical nonlinear neutral differential equations of third-order via comparison principles ⋮ Unnamed Item ⋮ Oscillation criteria for weakly superlinear differential equations of even order ⋮ Unnamed Item ⋮ Asymptotic properties of third-order delay trinomial differential equations ⋮ Oscillation of second-order quasilinear retarded difference equations via canonical transform ⋮ On the spectrum of a quasi-differential boundary value problem of the second-order ⋮ Improved oscillation criteria for second order quasilinear dynamic equations of noncanonical type ⋮ Oscillation results via comparison theorems for fourth-order delay three-terms difference equations ⋮ Oscillation criteria for noncanonical neutral Emden-Fowler differential equations ⋮ Asymptotic properties of the third order delay differential equations ⋮ Oscillation criteria for semilinear metaharmonic equations in exterior domains ⋮ Nonlinear oscillation of higher-order functional differential equations with deviating arguments ⋮ Oscillation of third order trinomial delay differential equations ⋮ Asymptotic behavior of oscillatory solutions of a differential equation with deviating arguments ⋮ Sign properties of Green's functions for disconjugate dynamic equations on time scales. ⋮ Properties of minors of the Wronskian for solutions of \(L_ ny+p(x)y=0\) as related to (k,n-k) disfocality ⋮ Existence of slow oscillations in functional equations ⋮ Analytic theory of finite asymptotic expansions in the real domain. Part I: Two-term expansions of differentiable functions ⋮ Unnamed Item ⋮ On properties of third-order differential equations via comparison principles ⋮ The problem of differentiating an asymptotic expansion in real powers. II: Factorizational theory ⋮ On Factorizations of Selfadjoint Ordinary Differential Operators ⋮ Oscillation of second-order nonlinear noncanonical differential equations with deviating argument ⋮ On a class of linear $n$-th order differential equations ⋮ On the oscillation of fourth-order delay differential equations ⋮ A singular quasilinear polyharmonic problem ⋮ Oscillation of \(n\)th order strongly noncanonical delay differential equations ⋮ Characterization of oscillation of fourth order functional differential equations with deviating arguments ⋮ Characterization of oscillation of fourth order functional differential equations with deviating arguments ⋮ Oscillation of second-order Emden-Fowler neutral differential equations with advanced and delay arguments ⋮ New oscillation criteria for second-order half-linear advanced differential equations ⋮ Comparison theorems of Hille-Wintner type for disconjugate linear differential equations ⋮ Unnamed Item ⋮ On nonoscillation of canonical or noncanonical disconjugate functional equations ⋮ Comparison theorems for the third order trinomial differential equations with delay argument ⋮ Unnamed Item ⋮ Oscillation of a class of third-order neutral differential equations with noncanonical operators ⋮ Oscillatory solutions and extremal points for a linear differential equation ⋮ Unnamed Item ⋮ Oscillation of strongly noncanonical equations ⋮ Oscillation results for third-order semi-canonical quasi-linear delay differential equations ⋮ Oscillation properties of solutions of second order neutral dynamic equations of non-canonical type on time scales ⋮ On quick oscillations in functional equations with deviating arguments ⋮ Generalized disconjugacy and comparison theorems ⋮ Oscillation of second-order half-linear neutral advanced differential equations ⋮ Oscillation Properties of Perturbed Disconjugate Equations ⋮ Some properties of third order differential operators ⋮ Unnamed Item ⋮ Asymptotic properties of differential equations with deviating argument ⋮ Integral comparison theorems and extremal points for linear differential equations ⋮ Boundedness of solutions of a class of higher order ordinary differential equations ⋮ Oscillation of third-order differential equations with noncanonical operators ⋮ Asymptotic solutions of semilinear elliptic equations ⋮ Properties of disconjugate linear differential operators ⋮ Comparable solutions to \(n\)th-order linear difference equations ⋮ On existence of nonoscillatory solutions in forced nonlinear differential equations

Cites Work

• Disconjugacy
• Disconjugate $n$th order differential equations and principal solutions
• Principal Solutions of Disconjugate n-th Order Linear Differential Equations
• Asymptotic Behaviour of Disconjugate nth Order Differential Equations
• Corrigendum and Addendum: Principal Solutions of Disconjugate n-th Order Linear Differential Equations
• Disconjugacy Tests for Singular Linear Differential Equations

This page was built for publication: Canonical Forms and Principal Systems for General Disconjugate Equations