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Meromorphic solutions of q-shift difference equations

100%
Liu K., Qi X.-G.
Annales Polonici Mathematici
|
2011
|
tom 101
|
nr 3
215-225
EN
We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.
2
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Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes

81%
Cao T.-B., Liu K., Cao H.-Z.
Annales Polonici Mathematici
|
2013
|
tom 107
|
nr 2
153-166
EN
The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from $ℂ^{m}$ into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.
3
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The zero distribution and uniqueness of difference-differential polynomials

81%
Liu K., Liu X.-L., Yang L.-Z.
Annales Polonici Mathematici
|
2013
|
tom 109
|
nr 2
137-152
EN
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
4
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On existence of a unique generalized solution to systems of elliptic PDEs at resonance

81%
Qiao T., Li W., Liu K., Wu B.
Annales Polonici Mathematici
|
2014
|
tom 110
|
nr 1
25-31
EN
The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.
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