Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates

From MaRDI portal
Publication:3778972

DOI10.1112/jlms/s2-37.121.88zbMath0638.30030OpenAlexW2048157048MaRDI QIDQ3778972

Gary G. Gundersen

Publication date: 1988

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/jlms/s2-37.121.88




Related Items

Subnormal solutions of second order linear differential equations with periodic coefficientsOn the hyper-order of solutions of two class of complex linear differential equationsThe complex oscillation theory of \(f^{\prime\prime} +Af^ \prime +Bf=F\), where \(A,B,F\not\equiv 0\) are transcendental meromorphic functionsBrück conjecture with hyper-order \(\sigma_{\mathbf {2}}(f) < \mathbf {1}\) and linear differential polynomialsOn the meromorphic solutions of linear differential equations on the complex planeOn meromorphic solutions of some linear differential equations with entire coefficients being Fabry gap seriesSome results of certain types of difference and differential equationsOn the hyper exponent of convergence of zeros of \(f^{(j)}-{\varphi}\) of higher order linear differential equationsGrowth and fixed points of meromorphic solutions of nonhomogeneous linear differential equationsOscillatory solutions of nonhomogeneous linear differential equationsOn the growth of solutions of a class of second-order complex differential equationsNon-real zeroes of real entire derivativesOn the iterated exponent of convergence of solutions of linear differential equations with entire and meromorphic coefficientsOn the exact forms of meromorphic solutions of certain non-linear delay-differential equationsComplex oscillation of higher-order linear differential equations with coefficients being lacunary series of finite iterated orderFurther results on certain type of nonlinear difference polynomialsThe deficiencies of meromorphic solutions of certain algebraic differential equationsAn entire function sharing a polynomial with its derivativesZeros of solutions of certain second order linear differential equationThe possible orders of growth of solutions to certain linear differential equations near a singular pointNonhomogeneous linear differential equations with entire coefficients having the same order and typeZeros of derivatives of meromorphic functionsNon-real zeros of derivatives of meromorphic functionsSharing set and normal families of entire functionsResults on meromorphic solutions of linear difference equationsRelation between small functions with differential polynomials generated by solutions of linear differential equationsOn subnormal solutions of periodic differential equationsOscillation theorem for higher-order linear differential equations with periodic coefficientsOn the iterated exponent of convergence of zeros of \(f^{(j)}(z)-{\varphi}(z)\)On the growth of solutions of second order linear differential equations with extremal coefficientsRelations between solutions of differential equations and small functionsHyper-order and fixed points of meromorphic solutions of higher order linear differential equationsOn Picard value problem of some difference polynomialsZeros of derivatives of real meromorphic functionsNonexistence of a subnormal solution of certain second order periodic differential equationsOn interpolating Blaschke products and Blaschke-oscillatory equationsNew findings on the Bank-Sauer approach in oscillation theoryEntire functions sharing an entire function of smaller order with their shiftsSome oscillation results of higher-order linear differential equations with meromorphic coefficientsDifferential polynomials generated by solutions of \(f^{{\prime}{\prime}}+a(z)f = F\)Numbers of subnormal solutions for higher order periodic differential equationsThe zeros on complex differential-difference polynomials of certain typesOn the complex oscillation of meromorphic solutions of nonhomogeneous linear differential equations with meromorphic coefficientsInfinite growth of solutions of second order complex differential equations with entire coefficient having dynamical propertyExponential polynomials in the oscillation theoryOn the zeros of certain linear differential polynomialsEntire functions sharing one or two finite values CM with their shifts or difference operatorsEntire functions that have the same fixed points with their first derivatives.The zeros of \(ff-b\)On the growth of solutions of a class of higher order linear differential equations with extremal coefficientsOscillation of solutions of linear differential equationsOn the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex planeOn the dependent property of solutions for general higher order periodic differential equationSolution of a differential equation and its applicationsThe radial oscillation of entire solutions of complex differential equationsInfinite growth of solutions of second order complex differential equationSome results on the complex oscillation theory of second order linear differential equationsNevanlinna theory of the Askey-Wilson divided difference operatorA note on the growth of solutions of second-order complex linear differential equationsGrowth of solutions of higher order complex linear differential equationThe Schwarzian derivative and the Wiman-Valiron propertyOn the growth of solutions of certain higher-order linear differential equationsBank-Laine functions, the Liouville transformation and the Eremenko-Lyubich classLogarithmic derivative estimates of meromorphic functions of finite order in the half-planeOn the relationship between the lower order of coefficients and the growth of solutions of differential equationsEntire functions sharing a non-zero value with their derivativesDerivatives of meromorphic functions of finite orderOn the growth of solutions of some second-order linear differential equationsA note on meromorphic functions that share a set with their derivativesOn the growth of solutions to the complex differential equation \(f^{\prime \prime} + Af^{\prime} + Bf = 0\)Real meromorphic functions and linear differential polynomialsA note on the Brück conjectureReal meromorphic functions and a result of Hinkkanen and RossiGrowth of solutions of three order differential equationsOn the growth of solutions of some higher order linear differential equations.Relation between differential polynomials and small functionsOrder and hyper-order of solutions of second order linear differential equationsUnicity of entire functions and a related problemOn the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimateOn hyper-order of solutions of higher order linear differential equations with meromorphic coefficientsOn Petrenko's deviations and second order differential equationsZero distribution of some shift polynomialsEntire functions sharing one finite value with their derivatives in some angular domainsZeros and fixed points of the linear combination of shifts of a meromorphic functionThe zero and order of some second order linear differential equations with transcendental meromorphic coefficientsGeneralization of Pólya's zero distribution theory for exponential polynomials, and sharp results for asymptotic growthThe growth of solutions to second-order linear differential equations with meromorphic coefficientsSome further results on the zeros and growths of entire solutions to second order linear differential equationsEntire functions that share one value with one or two of their derivativesThe growth of solutions of non-homogeneous linear differential equationsOn the simple connectivity of Fatou componentsGrowth of solutions of nonhomogeneous linear differential equationsSome unity results on entire functions and their difference operators related to 4 CM theoremSubnormal solutions of second-order nonhomogeneous linear differential equations with periodic coefficientsOn the hyper-order of meromorphic solutions to linear differential equationsNon-real zeros of linear differential polynomialsOn the uniqueness problems of meromorphic functions and their linear differential polynomialsUniqueness of entire function sharing a small function with its derivativeIntegral means of the logarithmic derivative of Blaschke productsThe growth of solutions to higher order differential equations with exponential polynomials as its coefficientsZero distribution of some delay-differential polynomialsThe zero, pole and order of meromorphic solutions of differential equations with meromorphic coefficientsSome results on the complex oscillation for higher order homogeneous linear differential equationsNonexistence of finite order solutions of certain second order linear differential equationsDifferential polynomials generated by solutions of second order non-homogeneous linear differential equationsLinear differential polynomials in zero-free meromorphic functionsA generalisation of the Bank-Laine propertyThe growth of linear differential equations and their applicationsNon-real zeros of derivatives of real meromorphic functionsLinear differential equations with entire coefficients of \([p,q\)-order in the complex plane] ⋮ On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equationsAn application of the spread relation to differential equationsCompletely regular growth solutions of second order complex linear differential equationsUnnamed ItemGrowth of solutions of non-homogeneous linear differential equations and its applicationsUnnamed ItemSome results on the entire function sharing problemDual exponential polynomials and a problem of OzawaOn the zeros of second order linear differential polynomialsRelationship between entire functions and their derivatives sharing small function except a setUnnamed ItemEntire function sharing a small function with its mixed-operatorsOn \([p,q_{,\varphi }\)-order and complex differential equations] ⋮ On the oscillation of certain second-order linear differential equationsGrowth of solutions of complex differential equations with solutions of another equation as coefficientsGrowth of solutions of complex differential equations with entire coefficients having a multiply-connected Fatou componentOn the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations in terms of (p,q)-orderLower order and limiting directions of Julia sets of solutions to second order differential equationsValue distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theoryEntire solutions of higher order differential equations with entire coefficients having the same orderOn entire function \(e^{p(z)}\int_0^z \beta (t)e^{-p(t)}dt\) with applications to Tumura-Clunie equations and complex dynamicsOn zeros and fixed points of differences of meromorphic functionsOn the growth of solutions of higher order linear homogeneous and non-homogeneous differential equationsA continuous transition from \(\mathcal{E} \)-sets to \(R\)-sets and beyondTrajectories escaping to infinity in finite timeGrowth of solutions of certain higher order linear differential equationsON GROWTH PROPERTIES OF TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF HIGHER ORDEROn a question of Gundersen concerning the growth of solutions of linear differential equationsUnnamed ItemZero separation results for solutions of second order linear differential equationsUnnamed ItemGROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANEWeakly repelling fixpoints and the connectivity of wandering domainsUnnamed ItemUnnamed ItemUnnamed ItemOn the growth of solutions of some higher order linear differential equations with meromorphic coefficientsBank-Laine functions with sparse zerosThe uniqueness of the entire functions whose \(n\)-th powers share a small function with their derivativesOn subnormal solutions of second order linear periodic differential equationsOn the growth of meromorphic solutions of some higher order linear differential equationsOn the meromorphic solutions of linear differential equationsOn the complex oscillation of higher order linear differential equations with meromorphic coefficientsOn the growth of solutions of a class of higher order linear differential equations with coefficients having the same orderProperties of differences of meromorphic functionsNon-real zeros of higher derivatives of real entire functions of infinite orderLower estimates of the growth order of solutions to the second Painlevé hierarchyOn complex oscillation property of solutions for higher-order periodic differential equationsThe possible orders of solutions of linear differential equations with polynomial coefficientsUnnamed ItemUnnamed ItemGrowth of solutions of second order linear differential equationsEntire solutions of differential equations with finite order transcendental entire coefficientsDifference analogue of Cartan's second main theorem for slowly moving periodic targetsLower Bound Estimates of the Order of Meromorphic Solutions to Non-Homogeneous Linear Differential-Difference EquationsEntire functions that share a polynomial with their derivativesSolution of a problem of Edwards and HellersteinSome results on the solutions of higher-order linear differential equationsUnnamed ItemGrowth of solutions of second order linear differential equationsOscillation result for some non-homogeneous linear differential equations and its applicationMeromorphic solutions of certain difference equations of first orderON THE BRÜCK CONJECTUREOn Zeros and Growth of Solutions of Second Order Linear Differential EquationsEntire functions that share a small function with their derivativesFinite Order Solutions of Second Order Linear Differential EquationsOn the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functionsZero distribution of solutions of complex linear differential equations determines growth of coefficientsEntire functions that share a set with their derivativesLower order and Baker wandering domains of solutions to differential equations with coefficients of exponential growthA Survey on a Conjecture of Rainer BrückOn interpolation problem with derivative in the space of entire functions with fast-growing interpolation knotsComplex oscillation and nonoscillation resultsThe growth of meromorphic solutions for a class of higher-order linear differential equationsFurther results about uniqueness of meromorphic functions sharing a set with their derivativesFinite Order Solutions of Second Order Linear Differential EquationsGrowth of solutions of second order complex linear differential equations with entire coefficientsOn the growth and fixed points of solutions of second order differential equations with meromorphic coefficientsOn the number of linearly independent admissible solutions to linear differential and linear difference equationsInfinite Order of Growth of Solutions of Second Order Linear Differential EquationsMeromorphic solutions to linear differential equations with entire coefficients of [p,q-order]