Finite Order Solutions of Second Order Linear Differential Equations

DOI10.2307/2001061zbMath0634.34004OpenAlexW4232814799MaRDI QIDQ3772528

Gary G. Gundersen

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2001061

zbMATH Keywords

examplessecond order differential quation

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Growth and boundedness of solutions to ordinary differential equations (34C11) Ordinary differential equations in the complex domain (34M99)

Related Items (58)

Research questions on meromorphic functions and complex differential equations ⋮ Subnormal solutions of second order linear differential equations with periodic coefficients ⋮ On difference equations concerning Schwarzian equation ⋮ Growth of meromorphic solutions of certain types of \(q\)-difference differential equations ⋮ Growth of meromorphic solutions to some complex functional equations ⋮ On meromorphic solutions of some linear differential equations with entire coefficients being Fabry gap series ⋮ Completely regular growth solutions of second order complex linear differential equations ⋮ Dual exponential polynomials and a problem of Ozawa ⋮ On the exact forms of meromorphic solutions of certain non-linear delay-differential equations ⋮ The deficiencies of meromorphic solutions of certain algebraic differential equations ⋮ Some properties of solutions of a class of systems of complex \(q\)-shift difference equations ⋮ Unnamed Item ⋮ On \([p,q_{,\varphi }\)-order and complex differential equations] ⋮ On the Growth and Oscillation of Fixed Points of Solutions of Linear Differential Equations with Meromorphic Coefficients ⋮ The growth of solutions of systems of complex \(q\)-shift difference equations ⋮ Growth of solutions of complex differential equations with entire coefficients having a multiply-connected Fatou component ⋮ Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory ⋮ On the growth of solutions of second order linear differential equations with extremal coefficients ⋮ A continuous transition from \(\mathcal{E} \)-sets to \(R\)-sets and beyond ⋮ Entire functions sharing a finite set with their difference operators ⋮ On finite-order meromorphic solutions of a class containing a difference Painlevé I equation ⋮ Unnamed Item ⋮ Numbers of subnormal solutions for higher order periodic differential equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Oscillation of solutions of linear differential equations ⋮ On the growth of solutions of some higher order linear differential equations with meromorphic coefficients ⋮ Entire functions sharing an entire function of smaller order with their difference operators ⋮ On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations ⋮ On subnormal solutions of second order linear periodic differential equations ⋮ Milloux inequality of nonlinear difference monomials and its application ⋮ On the growth order of solutions of linear differential equations in a sector of the unit disk ⋮ Some oscillation theorems for higher order linear differential equations with entire coefficients of small growth ⋮ On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane ⋮ The radial oscillation of entire solutions of complex differential equations ⋮ Growth of solutions of higher order complex linear differential equation ⋮ On the relationship between the lower order of coefficients and the growth of solutions of differential equations ⋮ Unnamed Item ⋮ Entire solutions of differential equations with finite order transcendental entire coefficients ⋮ On the growth of solutions to the complex differential equation \(f^{\prime \prime} + Af^{\prime} + Bf = 0\) ⋮ Linear differential equations with coefficients in weighted Bergman and Hardy spaces ⋮ Growth of solutions of three order differential equations ⋮ Order and hyper-order of solutions of second order linear differential equations ⋮ Deficient values of solutions of linear differential equations ⋮ On properties of meromorphic solutions for difference Painlevé equations ⋮ On hyper-order of solutions of higher order linear differential equations with meromorphic coefficients ⋮ On Petrenko's deviations and second order differential equations ⋮ Zero distribution of some shift polynomials ⋮ The zero and order of some second order linear differential equations with transcendental meromorphic coefficients ⋮ Weighted Bergman spaces induced by rapidly incresing weights ⋮ Zero distribution of solutions of complex linear differential equations determines growth of coefficients ⋮ Solutions of higher order linear differential equations in an angle ⋮ The growth of solutions of non-homogeneous linear differential equations ⋮ Order reduction method for linear difference equations ⋮ Linear differential equations in the unit disc with analytic solutions of finite order ⋮ Growth of solutions of second order complex linear differential equations with entire coefficients ⋮ On the hyper-order of solutions to some second-order linear differential equations ⋮ Infinite Order of Growth of Solutions of Second Order Linear Differential Equations

Cites Work

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• Non-existence of finite order solutions of \(w+e^{-z}w'+Q(z)w=0\)
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• Zur Frage des Maximalbetrages der Lösungen linearer Differentialgleichungen zweiter Ordnung mit Polynomkoeffizienten
• On the Value Distribution Theory for Entire Solutions of Second-Order Linear Differential Equations
• Second Order Differential Equations with Transcendental Coefficients
• On the oscillation of solutions of certain linear differential equations in the complex domain
• On the question of whether f″+ e^−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order
• Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates
• [https://portal.mardi4nfdi.de/wiki/Publication:4740850 On the Oscillation Theory of f � � + Af = 0 where A is Entire]
• Subnormale Lösungen der Differentialgleichung: w” + p(e^z)w’ + q(e^z) w + 0

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