Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equat...Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations.展开更多
Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference...Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.展开更多
In this paper,we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameterαin the nonlinear term in the following parabo...In this paper,we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameterαin the nonlinear term in the following parabolic equationh_(t)+h_(xxxx)+∂_(xx)|h_(x)|^(α)=f.It is shown that when 5/3≤α<7/3,the 3α-5/α−1-dimensional parabolic Hausdorff measure of S is zero,which generalizes the recent corresponding work of Ozánski and Robinson in[SIAM J.Math.Anal.,51,228–255(2019)]forα=2 and f=0.The same result is valid for a 3D modified Navier–Stokes system.展开更多
基金supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations.
基金supported by the National Natural Science Foundation of China(10471067)NSF of Guangdong Province(04010474)
文摘Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.
基金the National Natural Science Foundation of China(Grant Nos.11971446,11601492,11771423 and12071113)Natural Science Foundation of He’nan(Grant No.232300421077)Research Start-up Funding Program of Hangzhou Normal University(Grant No.4235C50223204065)。
文摘In this paper,we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameterαin the nonlinear term in the following parabolic equationh_(t)+h_(xxxx)+∂_(xx)|h_(x)|^(α)=f.It is shown that when 5/3≤α<7/3,the 3α-5/α−1-dimensional parabolic Hausdorff measure of S is zero,which generalizes the recent corresponding work of Ozánski and Robinson in[SIAM J.Math.Anal.,51,228–255(2019)]forα=2 and f=0.The same result is valid for a 3D modified Navier–Stokes system.
