In the last class of my subject of mathematics applied to biology the teacher proposed to us to model the density of certain substance. After several hypotheses, that I have decided to omit here in order to make the question more concise, I have obtained the following functional equation: $$-Af(x)^2+Bf(x)-C\int_{B(x,1)}f(y)dy=0,$$ where A,B,C are positive constants and $f:\mathbb{R^2}\to\mathbb{R}$ indicates the density in each point of the plane. In order to know if the equation that I have found makes sense I was trying to know some solutions. However, I am not able to find solutions that are not constant. Does anyone know of a method for finding solutions to equations like this? I could set some restriction on the parameters if necessary.
2026-02-24 13:47:27.1771940847
Non constant solutions of the following equation
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