Simple integral equation

Question

There is a simple integral equation: $$\int_0^\infty p(s) ds = 1- \frac{1}{\lambda}p(0).$$ Do you know how to solve it for $p(0)$ given we know $p(s)$ for $s>0$? Or maybe some references to methods how to solve it?

Answer 1

$$\int_0^\infty p(s) ds = 1- \frac{1}{\lambda}p(0)\implies p(0)=\lambda\left(1-\int\limits_0^\infty p(s)ds\right)\ldots\ldots?$$