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http://dx.doi.org/10.4134/CKMS.2015.30.4.447

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)

Publication Information

Communications of the Korean Mathematical Society / v.30, no.4, 2015 , pp. 447-456 More about this Journal

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.

Keywords

differential-difference equation; Fermat type q-difference differential equations; transcendental entire solution; finite order;

Citations & Related Records

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