Existence Of Entire Solutions For Fermat Type Differential Difference Equations And Q-differential Difference Equations

This dissertation mainly studies the existence of solutions of two kinds of nonlinear differential-difference equations by using the Hadamard factorization theorem in the Nevanlinna value distribution theory.The main contents of this dissertation include:Chapter 1 The introduction mainly introduces the background and significance of the research.Chapter 2 Preliminary knowledge is mainly introduced the basic knowledge of Nevanlinna theory and Knowledge of complex differential and difference fields.Chapter 3 We study the existence and exact expression of solutions of fermat type differential difference equations ω"（z）²+[P（z）（d1ω（z+c）+d0ω（z））)]²=Q（z）and fermat type q-difference differential equations ω’（z）²+[A（d1ω（qz）+d0ω（z））]²=Q（z）where P（z）,Q（z）are nonzero polynomials,q,A,d₀,d₁ are nonzero constants;Chapter 4 summary and follow-up work.