Remarks on Meromorphic Solutions of Some Delay-Differential Equations

Laine, Ilpo; Latreuch, Zinelaâbidine

doi:10.1007/s10476-022-0172-4

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2023

2024

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Cited by 2 publications

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“…outside a possible exceptional set F of finite logarithmic measure (see [4]). Here, S(r, f ) is any quantity that satisfies S(r, f ) = o(T (r, f )) as r → ∞ outside a set F .…”

Section: Introductionmentioning

confidence: 99%

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On value distribution of certain delay-differential polynomials

Li¹,

Yang²

2023

ScienceAsia

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Given an entire function f of finite order ρ, let L(z, f ) = m j=0 b j (z) f (k j ) (z+c j ) be a linear delay-differential polynomial of f with small coefficients in the sense of O(r λ+ ) + S(r, f ), λ < ρ. Provided α and β are similar small functions, we consider the zero distribution of L(z, f ) − α f n − β for n 3 and n = 2, respectively. Our results are improvements and complements of Chen

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“…outside a possible exceptional set F of finite logarithmic measure (see [4]). Here, S(r, f ) is any quantity that satisfies S(r, f ) = o(T (r, f )) as r → ∞ outside a set F .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, several articles (see [4,[6][7][8][9][10][11][12][13][14][15][16][17][18]) have focused on complex differences, giving many difference analogues in value distribution theory of meromorphic functions.…”

Section: Introductionmentioning

confidence: 99%

On value distribution of certain delay-differential polynomials

Li¹,

Yang²

2023

ScienceAsia

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Notes on Fermat-Type Difference Equations

LAINE,

LATREUCH

2024

Bull. Aust. Math. Soc.

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We consider the existence problem of meromorphic solutions of the Fermat-type difference equation $$ \begin{align*} f(z)^p+f(z+c)^q=h(z), \end{align*} $$ where $p,q$ are positive integers, and h has few zeros and poles in the sense that $N(r,h) + N(r,1/h) = S(r,h)$ . As a particular case, we consider $h=e^g$ , where g is an entire function. Additionally, we briefly discuss the case where h is small with respect to f in the standard sense $T(r,h)=S(r,f)$ .

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Remarks on Meromorphic Solutions of Some Delay-Differential Equations

Cited by 2 publications

References 20 publications

On value distribution of certain delay-differential polynomials

On value distribution of certain delay-differential polynomials

Notes on Fermat-Type Difference Equations

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