Study on solutions of the systems of complex product-type PDEs with more general forms in ℂ2

With the help of the Nevanlinna theory and the Hadamard factorization theory of meromorphic functions, we mainly give a description of the existence and the forms of the transcendental entire solutions of several product-type complex partial differential equations systems and where , , ; , and and are the polynomials in . More importantly, we list some examples to explain that our results about the forms of solutions of such systems are precise to some extent.