I'm trying to solve this form of Fredholm equation:

$$
g(v)=f_1(v)+\int\limits_{0}^{v_\mathrm{th}} g(v_s)\frac{e^{-\tfrac{\big[(v-v_\mathrm{init})-(1-v_\mathrm{leak})(v_s-v_\mathrm{init})\big]^2}{2v_\mathrm{step}^2}}+e^{-\tfrac{\big[(v-v_\mathrm{init})+(1-v_\mathrm{leak})(v_s-v_\mathrm{init})\big]^2}{2v_\mathrm{step}^2}}}{\sqrt{2\pi}v_\mathrm{step}}\mathrm{d} v_s,
$$
where, 
* $v_\mathrm{init}$, $v_\mathit{th}$, $v_\mathrm{step}$, $v_\mathrm{leak}$ are constant and
* $f_1$ has the following form:
$$
f_1(v)=\frac{e^{-\tfrac{(v-v_\mathrm{init})^2}{2v_\mathrm{step}^2}}+e^{-\tfrac{(v+v_\mathrm{init})^2}{2v_\mathrm{step}^2}}}{\sqrt{2\pi}v_\mathrm{step}}
$$
Are there any method or theorm that can solve this problem?

Since I'm freshman in university, it's very challenging for me. But I really want to untangle this problem.

Can you help me to solve this kind of equation or let me know what theory I should study in order to start attaching this problem?

I would be grateful if you could just give me directions, so I can know where to start studying. Sorry for my bad English.



  [1]: https://i.sstatic.net/jM0Au.png
  [2]: https://i.sstatic.net/59oBs.png