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ENTIRE SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATION AND FERMAT TYPE q-DIFFERENCE DIFFERENTIAL EQUATIONS

  • CHEN, MIN FENG (LMIB and School of Mathematics and Systems Science Beihang University) ;
  • GAO, ZONG SHENG (LMIB and School of Mathematics and Systems Science Beihang University)
  • Received : 2015.05.12
  • Published : 2015.10.31

Abstract

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

Acknowledgement

Supported by : National Natural Science Foundation of China

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