[PDF] Top 20 The properties of solutions of certain type of difference equations

... where L(f ) is a linear differential polynomial in f with polynomial coefficients, p(z) is a non-vanishing polynomial, h(z) is an entire function, and n is an integer such that n ≥ . Subsequently, several papers have ... See full document

... the field of small functions with respect to w. A meromorphic solution w of a difference equation is called admissible if all coefficients of the equation are in S(w). For example, if a difference equation has only rational ... See full document

... Notations Given a meromorphic function f , recall that α ≡ , ∞ is a small function with respect to f , if T (r, α) = S(r, f ), where S(r, f ) denotes any quantity satisfying S(r, f ) = o{T (r, f )} as r → +∞, possibly ... 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

... difference equations of type (1.4;δ), the study of higher-order equations, and in particular third-order equations of type ...for equations with deviating ...behavioral ... See full document

... On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations Zhang Advances in Difference Equations (2016) 2016 300 DOI 10 1186/s13662 016 1030 0 R E S E A R C[.] ... 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

... the solutions of certain types of generalized  -difference equations, in particular, the generalized Clairauts  - difference equation, generalized Euler  -difference equation ... See full document

... meromorphic solutions of finite order, then either w satisfies a difference Riccati equation, or ...difference equations, which contains many integrable equations, especially the difference Painlevé I, II ... See full document

... of solutions with a specified local asymptotic behavior for the above equation (see also ...Leray-Schauder type fixed point theorem is the appropriate tool to obtain a good result for this nonlocal ... See full document

... Gronwall-Bellman type inequalities. These inequalities involve Gronwall-Bellman type differential and integral inequalities [13-18], retarded inequalities [19-23], difference inequalities [24-28], ... See full document

... meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their meromorphic solutions, and give a number of examples to show what our ... See full document

... nonlinear difference equation was studied intensively by ...of solutions of nonlinear neutral delay difference ...delay difference equation of the form ∆ ( ∆ 2 ( ∆ ( + ) ) ) + ( ) = ... See full document

... differential equations in the complex plane C, it is always an interesting and quite difficult problem to prove the existence or uniqueness of the entire or meromorphic solution of a given ...meromorphic ... See full document

... various equations like ordinary and partial differen- tial equations [3–6], difference equations [7–9], dynamic equations on time scales [10–14], and fractional differential (difference) ... See full document

... On the solutions of a max type system of difference equations with period two parameters Su et al Advances in Difference Equations (2018) 2018 358 https //doi org/10 1186/s13662 018 1826 1 R E S E A R[.] ... See full document

... x (t) = A(t)x(t) + B(t)x(t − τ ) + f (t), t > 0, (2) where A, B Î C( ℝ , ℝ m×m ) and f Î C( ℝ , ℝ m ) are periodic functions of period ω and τ >0 is a fixed real number. It was shown that the required condition ... See full document

... Meromorphic solutions of complex differential equations and complex difference equations plays a prominent role in the field of Complex ...analysis. Solutions of such equations ... See full document

... nice properties only for numbers whose real parts lie in [0, ...interesting properties of the fractional inte- grals and ...these properties, the following concepts for the new type fractional ... See full document

... various properties of solu- tions of differential and difference equations such as oscillation theory, disconjugacy, and eigenvalue problems (see [1, 2, 5–7, 9, 13, 15, 21, 24, 27–29, 37, 39, 45, 48, 57, 59] ... See full document