A physics problem I'm working on involves solving a partial differential equation of a type I've never encountered before. I'm not sure what the name for it is, which makes researching possible numerical techniques very difficult, so I'm hoping someone has seen something similar before so they could point me towards any existing literature.
The form of the partial differential equation in question is $\frac{\partial^{2} T(E,x)}{\partial x^{2}} + f(E)T(E,x) + g(E)\int_0^c h(E)T(E,x) dE = 0 $, where f(E), g(E) and h(E) are known functions of E (energy), and c is a constant.
The integral is really just a function of x, but I'm not sure how it can be solved without first knowing T(E,x), which can't be solved for exactly without knowing the solution to the integral first.
Is there a name for this kind of equation? I suspect there are similar problems out there, but I don't know what the proper name for them is. Any help would be greatly appreciated.