Figure 3.
(a–c): Typical sketches of f(Λ) and g(Λ;L1,L2) for 0<γ1<γ2<γ3 with both L1,2 respectively, small, intermediate and large. Equation (2.27) has, respectively, one, two and three positive solutions. (d): The first, respectively second, root of f(Λ)=g(Λ;L1,L2) emerges from the essential spectrum at Λ=0 (for increasing L1,2) at the curves ω1,2(L1,L2) where g(0;L1,L2)=f′′(0). In other words, g(0;L1,L2)<f′′(0) in the grey areas and (2.27) has one, respectively, three, positive solutions, while g(0;L1,L2)>f′′(0) in the intermediate white area and (2.27) has two positive solutions.