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Let K be a complete ultrametric algebraically closed field of characteristic π. Let P,Q be in K[x] with P′Q′ not identically 0. Consider two different functions f,g analytic or meromorphic inside a disk |x−a|<r (resp. in all K), satisfying P(f)=Q(g). By applying the Nevanlinna's values distribution Theory in characteristic π, we give sufficient conditions on the zeros of P′,Q′ to assure that both f,g are “bounded” in the disk (resp. are constant). If π≠2 and deg(P)=4, we examine the particular case when Q=λP (λ∈K) and we derive several sets of conditions characterizing the existence of two distinct functions f,g meromorphic in K such that P(f)=λP(g). 相似文献
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Chung-Chun Yang 《Proceedings Mathematical Sciences》1975,82(2):37-40
LetF M denote the class of univalent analytic functionsf in |z|<1 with the expansionf (z)=z+a 2 z 2+a 3 z 3+... and |f(z)|?M in |z|<1. In this note I derive a rough bound for alln-th coefficients and a more accurate bound for all the third coefficients of functionsf belonging toF M. 相似文献
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We prove a subspace theorem for homogeneous polynomial forms which generalizes Schmidt’s subspace theorem for linear forms.
Further, we formalize the subspace theorem into a form which is just the counterpart of a second main theorem in Nevanlinna’s
theorem, and also suggest a problem.
The work of the first author was partially supported by NSFC of China: Project. No. 10371064.
The second author was partially supported by a UGC Grant of Hong Kong: Project No. 604103. 相似文献
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Xiaoling Wang Chung-Chun Yang 《Journal of Mathematical Analysis and Applications》2006,324(1):373-380
We investigate the factorization of entire solutions of the following algebraic differential equations:
bn(z)finjn(f′)+bn−1(z)fin−1jn−1(f′)+?+b0(z)fi0j0(f′)=b(z), 相似文献
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This paper deals with some general irregular oblique derivative problems for nonlinear uniformly elliptic equations of second order in a multiply connected plane domain. Firstly, we state the well-posedness of a new set of modified boundary conditions. Secondly, we verify the existence of solutions of the modified boundary-value problem for harmonic functions, and then prove the solvability of the modified problem for nonlinear elliptic equations, which includes the original boundary-value problem (i.e. boundary conditions without involving undertermined functions data). Here, mainly, the location of the zeros of analytic functions, a priori estimates for solutions and the continuity method are used in deriving all these results. Furthermore, the present approach and setting seems to be new and different from what has been employed before.The research was partially supported by a UPGC Grant of Hong Kong. 相似文献
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