Lorentz-Einstein equation and Sturm Liouville Theory

[member 11137]

I first want to excuse me if it is the wrong place to post my question and if it is forbidden to ask such question on this forum because I know that personal research are not specially wellcome here. I don't want to disturb; I just want to learn more.
The question is: does it make sense to developp an essay in which I would try to recognize a set of four differential equations in observing the Lorentz-Einstein equation (LEE)? With other words does it make sense to look for a change of basis that would allow to read this LEE as a diff equ of second order ? And if I find one of these basis where it seems to be possible, is it correct to analyze the new formulation of the LEE with the Sturm Liouville Theory ?
One year ago I discovered the Connectivity Theory and I remarked that this latter obtain similar mathematical results than my approach, but through other ways.
Thank you for constructive remarks. Blackforest

 

[seratend]

What do you call "the Lorentz-Einstein equation"?

Seratend.

 

[member 11137]

On the left hand: ro. Du/ds where ro is the volumetric density of matter, u is the 4-speed vector, D the total derivative along the path s; on the right hand: [F].j the Lorentz force where [F] is the strenght field tensor and j the Lorentz current. Sorry I don't work with Latex or similar useful program (I will try to learn).