The Growth And Value Distribution Of Solutions Of Some Complex Linear Differential And Difference Equations

In this thesis,using the Nevanlinna's value distribution theory and the asymp-totic value theory of entire function,we mainly investigate the growth and value distribution of solutions of some complex linear differential and difference equa-tions.It consists of four chapters.In chapter 1,we briefly introduce the development history in the field of complex linear differential equations and complex difference equations,and the research background of this thesis.Some definitions and basic notations related to this thesis are also introduced.In chapter 2,we investigate the growth of solutions of the second order linear differential equations f" + A1(z)f' + A0(z)f = 0.Let A1(z)?h1eQ1(z)+ h2eQ2(z),where Qj(z)(j = 1,2)are polynomials of degree n(? 1)such that their leading coefficient have the same argument,hj are entire functions with order less than n,and let A0 be a transcendental entire function with lower order ?(A0)? n,it is proved that every nontrivial solution of such equations is of infinite order.Some estimates on hyper-order of its solutions are also obtained.In chapter 3,using the Nevanlinna's value distribution theory and the asymp-totic value theory of entire function,we investigate the growth of solutions of cer-tain higher order linear differential equations with entire coefficients.When there exists one coefficient being extremal for Denjoy's conjecture,we find some condi-tions on coefficients to guarantee that every nontrivial solution of such equations is of infinite order.In chapter 4,we investigate the growth and value distribution of meromorphic solutions of the type of linear difference equations An(z)f(z+cn)+…+A1(z)f(z+c1)+ A0(z)f(z)= 0 and An(z)f(z + cn)+… + A1(z)f(z + c1)+ A0(z)f(z)= F(z)with meromorphic coefficients,where Aj(z)= Pj(eA(z))+Qj(e-A(z))+Rj(z)(j =0,…,n),Rj.(z),F(z)(? 0)are meromorphic functions,Pj(z),Qj(z),A(z)are poly-nomials.