[PDF] Top 20 Properties of meromorphic solutions of Painlevé III difference equations

... A meromorphic solution w of a difference equation is called admissible if all coefficients of the equation are in ...non-rational meromorphic solutions are admissible; if an admissible solution is ... See full document

... the properties of meromorphic solutions of Painlevé III difference ...rational solutions of the equation assume only one form and the transcendental solutions have at most ... See full document

... In this paper, we shall assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions (see [13] , [20]). In ... See full document

... For the q-difference equation (.), Theorem C only considered the case when solutions have Borel exceptional zeros and poles. But how about the existence and growth of mero- morphic solutions of (.)? ... See full document

... ceptional value (also a Borel exceptional value) . It is natural to ask can the solutions of (.) have two Borel exceptional values? Corresponding to these questions, we obtain the following results as the ... See full document

... and meromorphic in the ...the meromorphic function f (z), and λ(f ) and λ(  f ) to denote, respectively, the exponents of convergence of zeros and poles of f ... See full document

... admissible meromorphic solution of finite order, then either ω satisfies a difference Riccati equation, or equation ...difference Painlevé equation or a linear difference ...of properties of difference ... See full document

... of meromorphic solutions of certain linear difference equations with meromorphic ...the properties of meromorphic solutions of a nonhomogeneous linear difference ... See full document

... difference equations have been got ...of meromorphic solutions of some difference equations, and several papers [, , –] deal with analytic properties of meromorphic ... See full document

... Remark . It is unlikely that most of the q-difference equations studied in this paper have meromorphic solutions due to the properties of the q-difference operator. The reason for this is the ... See full document

... We use Nevanlinna’s value distribution theory of meromorphic functions (see [1, 2]) as the main tool in the whole paper. In what follows, the growth order of w(z) is represented by σ (w) and the exponent of ... See full document

... In this paper, we use the basic notions in Nevanlinna theory of meromorphic functions, as found in []. In addition, we use δ(f ), λ(f ), and λ(  f ) to denote the order, and the exponents of the convergence of ... See full document

... same Painlevé equation or for ...new solutions by transformation. Specially, Painlevé equa- tion appeared in many applications and fields such as hydrodynamics, plasma physics, nonlinear optics, solid ... See full document

... w z + w z − = R z w z , (1.1) where R ( z ) is a nonzero rational function and m ∈ ± ± { 2, 1,0 } The Equation (1.1) comes from the family of Painlevé III equations which are given by Ron- kainen in ... See full document

... The Valiron-Mohon’ko identity [, ] is a useful tool to estimate the characteristic function of a rational function, the proof of which can be found in [, Theorem ..]. Lemma . Let w be a meromorphic ... See full document

... and meromorphic in the ...the meromorphic function f (z), and λ(f ) and λ(  f ) to denote the exponents of convergence of zeros and poles of f (z), ...a meromorphic function g is small with respect ... See full document

... Difference equations appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations having applications in biology, ecology, economy, physics, and so ... See full document

... The aim of this paper is to present some new Gronwall- Bellman type fractional integral inequalities and Volterra- Fredholm type fractional integral inequalities for the sake of researching qualitative and quantitative ... See full document

... greater than the others. Then, for any meromorphic solution of Eq. (1), we have σ (f ) ≥ σ + 1. The condition about type in Theorem D still means the growth of some coefficient is faster than the others, although ... See full document

... Remark . From the proof of Theorem ., we see that the restriction in Theorem . to p, q, and R may extend to small functions.. In fact, it is easy to find that the conclusion is vali[r] ... See full document