Left- (black line) and right- (red line) hand sides of Eq. (23) as a function of s/L, for three different situations with one, two, and three solutions. In these plots s₀ = 0.4/L (where the black line crosses zero), L = 10 H, l_t = L/50; ρ_t/ρ₀ = 100 (top panel), ρ_t/ρ₀ = ρ_tb/ρ₀ (middle panel), and ρ_t/ρ₀ = 200 (bottom panel). The value ρ_tb/ρ₀ ≈ 137.28 is obtained from Eqs. (23) and (24). The vertical dashed lines represent the edges of the domain of the variable s, namely s = l_t/2 and s = L − l_t/2.