[PDF] Top 20 Entire solutions of certain class of differential difference equations

... Thus, we obtain the desired result and finish the proof of this theorem. It is not difficult to see that a similar argument can be used to obtain the following result. Theorem . Let f be an entire solution of finite ... See full document

... Case , m = n ≥ . If m = n = , note that P(z) and Q(z) are non-constant polynomials, by Theorem D, we see that (.) has no transcendental entire solutions of finite order. If m = n ≥ , rewriting (.) as ... See full document

... (ii) Suppose that a finite order entire solution f (z) has infinitely many zeros and r(z) ≡ . We assume that all zeros of p(z) are in D = { z : | Re z | ≤ M, | Im z | ≤ M } , where M >  is some constant. From ... 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 ... See full document

... ordinary differential equations. Sometimes, obtaining exact solutions through the direct methods (analytical methods) for these systems seems difficult even if the exact solutions exist, hence ... 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

... function α IM, recently Wang has generalized Gundersen and Yang’s results, see []. In this paper, we consider the uniqueness of entire functions sharing a small function with their linear difference and ... See full document

... differential equations, we still need to define the notion of uniform semi-periodicity and prove that the associated Nemystkii operators map the set of semi-periodic sequences into ...semi-periodic solutions ... See full document

... symmetric solutions for very general f (see ...nonradial solutions of the above problem for some f (see ...that certain nice features inherent to the case p = 2 seem to be lost or at least di ffi cult ... See full document

... A finite value a is called the Picard exceptional value of f, if f - a has no zeros. The Picard theorem shows that a transcendental entire function has at most one Picard exceptional value, a transcendental ... See full document

... The current Clunie types of theorems regarding difference-differential polynomials are mainly useful or effective to deal with problems relating to entire or meromorphic solu- tions of finite order for certain ... See full document

... Sullivan [] proved that rational functions do not have wandering domains. However, transcendental meromorphic functions may have wandering domains (for example, see [–]), while many classes of meromorphic functions do ... See full document

... of solutions of certain class of generalized difference equations”, International Journal of Differential Equations and Applications, 2007, ... See full document

... The above theorem was derived by Hayman [] in . Later, he conjectured [] that Theorem A remains valid even if n =  or n = . Mues [] proved the result for n =  and the case n =  was proved by Bergweiler and ... See full document

... It becomes natural for us to ask the following question: Does the conclusion of Theo- rem 1.1 remains valid if the condition “u is a non-zero rational function and v is a non- constant polynomial” is replaced by a weaker ... See full document

... When Fn, x is subquadratic at infinity, as far as the authors are aware, there is no research about the existence of homoclinic solutions of 1.1. Motivated by the paper 16, the intention of this paper is that, ... See full document

... Difference equations have attracted the interest of many researchers in the last 20 years since they provided a natural description of several discrete models, in which the periodic solution problem is ... See full document

... differential equations had been ...differential equations play increasingly important roles in the modeling of engineer- ing and science ...differential equations have been investigated ... See full document

... Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and ...functional differential systems has come into ... See full document

... Definition Let : ( , ) → and x ∈ ( , ). (i) If for sufficiently small ℎ > 0, ∃ ( + ℎ) ( ), ∃ ( ) ( − ℎ) such that → ( ) ( ) = → ( ) ( ) = ′ ( ) holds, then is said to be (1) – differentiable. (ii) If for sufficiently ... See full document