SOLUTIONS OF COMPLEX NONLINEAR FUNCTIONAL EQUATIONS INCLUDING SECOND ORDER PARTIAL DIFFERENTIAL AND DIFFERENCE IN C2

This article is devoted to exploring the existence and the form of finite order transcendental entire solutions of Fermat-type second order partial differential-difference equations � partial differential 2f + & delta; partial differential 2f+ & eta; partial differential 2f )2+ f(z1 + c1, z2 + c2)2 = eg(z1,z2) partial differential z2 partial differential z2 1 2 partial differential z1 partial differential z2 and ( partial differential 2 f + & delta; partial differential 2f + & eta; partial differential 2f )2+ (f(z1 + c1, z2 + c2) - f(z1, z2))2 = eg(z), partial differential z2 partial differential z2 1 2 partial differential z1 partial differential z2 where & delta;, & eta; & ISIN; C and g(z1, z2) is a polynomial in C2. Our results improve the results of Liu and Dong [23], Liu et al. [24], and Liu and Yang [25]. Several examples confirm that the form of transcendental entire solutions of finite order in our results are precise.