Admissible meromorphic solutions of algebraic differential‐difference equations
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DOI: 10.1002/mma.5564
Abstract: By using Nevanlinna theory, we generalize a result given by Wittich to complex differential‐difference equations. The result obtained is that the differential‐difference equation in f which is of only one dominant term, has no admissible… read more here.
Keywords: difference; solutions algebraic; meromorphic solutions; difference equations ... See more keywords
Meromorphic solutions of recurrence relations and DRA method for multicomponent master integrals
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DOI: 10.1007/jhep04(2018)061
Abstract: A bstractWe formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique… read more here.
Keywords: recurrence; recurrence relations; relations dra; dra method ... See more keywords
Meromorphic Solutions of Certain Nonlinear Difference Equations
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DOI: 10.1007/s00025-021-01414-5
Abstract: Let $$p_1, p_2$$ be nonzero rational functions, $$\alpha _1, \alpha _2$$ be nonzero constants, and $$P_d(z, f)$$ be a difference polynomial in f of degree d. We prove that every finite order meromorphic solution of… read more here.
Keywords: nonlinear difference; difference equations; meromorphic solutions; difference ... See more keywords
On meromorphic solutions of a certain type of nonlinear differential equations
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DOI: 10.1007/s10114-017-6484-9
Abstract: We consider transcendental meromorphic solutions with N(r, f) = S(r, f) of the following type of nonlinear differential equations: $${f^n} + {P_{n - 2}}\left( f \right) = {p_1}\left( z \right){e^{{\alpha _1}\left( z \right)}} + {p_2}\left(… read more here.
Keywords: left right; type nonlinear; nonlinear differential; differential equations ... See more keywords
Entire and Meromorphic Solutions of the Functional Equation $$f^n+g^n+h^n=1$$fn+gn+hn=1 and Differential Equations
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DOI: 10.1007/s40315-018-0258-y
Abstract: In this paper, we study Fermat-type functional equations $$f^n+g^n+h^n=1$$fn+gn+hn=1 in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of… read more here.
Keywords: equation differential; differential equations; entire meromorphic; solutions functional ... See more keywords
On Meromorphic Solutions of Functional Equations of Fermat Type
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DOI: 10.1007/s40840-018-0613-1
Abstract: Take complex numbers $$\alpha ,\beta ,c,a_j,b_j$$α,β,c,aj,bj$$(j=0,1,2)$$(j=0,1,2) such that $$c\ne 0$$c≠0 and $$\begin{aligned} \mathrm{rank} \left( \begin{array}{ccc} a_{0} &{} a_{1} &{} a_{2}\\ b_{0} &{} b_{1} &{} b_{2}\\ \end{array} \right) =2. \end{aligned}$$ranka0a1a2b0b1b2=2.We show that if the following functional… read more here.
Keywords: end aligned; fermat type; meromorphic solutions; alpha beta ... See more keywords
Growth on Meromorphic Solutions of Differential–Difference Equations
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DOI: 10.1007/s40840-019-00753-5
Abstract: By using Nevanlinna theory and linear algebra, we show that the number one is a lower bound of the hyper-order of any meromorphic solution of a nonlinear differential–difference equation under certain conditions. read more here.
Keywords: solutions differential; growth meromorphic; difference equations; differential difference ... See more keywords
Meromorphic solutions of difference Riccati equations
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DOI: 10.1080/17476933.2016.1204605
Abstract: We are concerned with difference Riccati equations in the complex plane. We study the continuous limit of difference Riccati equations to differential Riccati equations, and compare asymptotic expansions of both of solutions. Some examples are… read more here.
Keywords: difference riccati; riccati equations; solutions difference; meromorphic solutions ... See more keywords
Existence of zero-order meromorphic solutions of certain q-difference equations
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DOI: 10.1186/s13660-018-1790-z
Abstract: AbstractIn this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f),$$ \bigl(f(qz)+f(z)\bigr) \bigl(f(z)+f(z/q)\bigr)=R(z,f), $$ where R(z,f)$R(z,f)$ is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution… read more here.
Keywords: existence zero; difference; zero order; meromorphic solutions ... See more keywords
Growth of meromorphic solutions of certain types of q-difference differential equations
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DOI: 10.1186/s13662-017-1072-y
Abstract: In this paper, relying on Nevanlinna theory of the value distribution of meromorphic functions, we mainly study meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their meromorphic… read more here.
Keywords: difference; difference differential; types difference; meromorphic solutions ... See more keywords
Meromorphic solutions of difference equations originated from Schwarzian differential equation
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DOI: 10.2298/fil2006003l
Abstract: Let f (z) be a meromorphic functions with finite order , R(z) be a nonconstant rational function and k be a positive integer. In this paper, we consider the difference equation originated from Schwarzian differential… read more here.
Keywords: originated schwarzian; differential equation; equation; meromorphic solutions ... See more keywords