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We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems$$\left\{\begin{array}{cc}-{\left[\phi \left(u^{\text{'}}\right)\right]}^{\text{'}}=\lambda u^p\left(1-{\displaystyle \frac{u}{N}}\right)\hfill & \text{in}(-L,L),\hfill \\ u(-L)=u\left(L\right)=0,\hfill \end{array}\right.$$ where $p>1$, $N>0$, $\lambda >0$ is a bifurcation parameter, $L>0$ is an evolution parameter, and $\phi \left(u\right)$ is either $\phi \left(u\right)=u$ or $\phi \left(u\right)=u/\sqrt{1-u^2}$. We prove that the corresponding bifurcation curve is $\subset$-shape. Thus, the exact multiplicity of positive solutions can be obtained.