| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 107 === Let three point charges locate at (1,0,0),(-1,0,0) and (u,v,0) with charge value s^3,k^3,1 respectively, then they create an electrostatic potential V for three point charges. By changing variables, we get two polynomial equations with two variables X,Y and four parameters S,K,u,v.
In this thesis we intend to find the real zero from that equation and we prove our theorems it by Sturm theorem and find the critical point.
We consider u=0 and v= √3 and obtain that has only one real zero for general K and S. For >0 and K>0 , we observe that the critical point inside of the triangle regions. When S = 1 or K = 1 the critical point on the symmetric line.
|
|---|
