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We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation fm(z)+gn(z)=1 with integers m,n≥2, from which other approaches to proving the little Picard theorem are discussed. [ABSTRACT FROM AUTHOR]

We investigate several quantitative properties of entire and meromorphic solutions to some differential-difference equations and generalised delay differential-difference equations. Our results are sharp in a certain sense as illustrated by several examples. [ABSTRACT FROM AUTHOR]

In this paper, we describe a second main theorem of holomorphic curves [ABSTRACT FROM AUTHOR]

A paper regarding the non-existence of finite order meromorphic solutions to the Fermat-type difference equation over the complex plane C is presented. Topics discussed in Nevanlinna theory, Weierstrass's elliptic function, and function analogues to the Fermat diophantine equations. Results of the description of a property of meromorphic solutions to equation in C is offered.

We establish a defect relation for algebraically non-degenerate meromorphic maps over generalized p-parabolic manifolds that intersect hypersurfaces in smooth projective algebraic varieties, extending certain results of H. Cartan, L. Ahlfors, W. Stoll, M. Ru, P. M. Wong and Philip P. W. Wong and others. [ABSTRACT FROM AUTHOR]

Abstract: By emplying the main ideas from G. Brosch, two results of R. Nevanlinna''s Four Value Theorem type on the unicity of meromorphic functions in the open complex plane sharing three distinct values, and a fourth value or a pair of values weakly are proved, which extend and generalize previous results of R. Nevanlinna, G.G. Gundersen, H. Ueda and G. Brosch. [Copyright &y& Elsevier]

Abstract: A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood–Yang''s conjecture and Mues'' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the relation between the characteristics of two meromorphic functions that share three weighted values, which improve the results of Q.C. Zhang. And through the results, two conjectures which proposed by Mues and Osgood-Yang are solved in a weaker condition. [Copyright &y& Elsevier]