How to solve a functional extremum problem where the boundary condition is inhomogeneous? let's say $$\begin{aligned}&\max_{F}\int_p^11-F(v)dv\\ s.t.& 1-F(p)-pF'(p)=0\\ &F(p) \text{ is a cumulative distribution function(CDF) over } [0,1]\end{aligned},$$ where $p\in(0,1)$. If the inhomogeneous boundary condition does not exist, I know how to solve this problem. Now with it, it seems very hard to evaluate.
2026-03-30 07:11:21.1774854681
Functional Extremum Problem with inhomgeneous boundary condition
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