Graph intersection and uniqueness results for some nonlinear elliptic problems (Q1183239)

Uniqueness and graph intersection properties are shown for positive solutions \(u\) of \((\varphi u')'+g(x,u) f(u)=0\), \(\varphi>0\), \(f\) concave, \(g\) increasing in \(u\), no sign for \(g\). Under certain assumptions, for example, it is shown that two distinct solutions can intersect at most once. The problem is motivated by PDEs of population genetics.