Homogenizing for Linear Non-Homogeneous Boundary Conditions of Class 1, 2 or 3
LU Li-zh · Journal of Shanxi Teachers University · 2001
Eigenfunction and Green′s function are the main methods to get the definite solutions of Mathematical physics problems, but the problem should have linear homogeneous conditions. If the problem has the non-homogeneous boundary conditions, an auxiliary function should be found to transfer it to be under the conditions of homogeneous boundary conditions. In the paper, firstly we discuss problems of stable non-homogeneous boundary conditions to get the general method and results of how to select the auxiliary function; then transform the results by transformation of parameter, and verify the results is applicable to problems of unstable non-homogeneous border conditions. At last we get the general method and solution to select an auxiliary function.