Classification and evolution of bifurcation curves for the one-dimensional perturbed Gelfand equation with mixed boundary conditions

Classification and evolution of bifurcation curves for a one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity

“…Note that, since ρ 1 < 2/5 ≤ρ ε by Lemma 3.8(i), we have that K 3 (ρ 1 , s) < 0 by (17). Hence the inequality lim ρ→(ρ1) + d dρ Ψ(ρ, q(ρ, c 1 )) < 0 holds for all 1/10 ≤ ε ≤ 1/5 if the following Claim B holds.…”

“…Liang and Wang [17,18] recently considered the classification and evolution of bifurcation curves of positive solutions for the one-dimensional perturbed Gelfand equation with the same Dirichlet-Neumann boundary conditions in (1) given by…”

Double bifurcation diagrams and four positive solutions of nonlinear boundary value problems via time maps

“…Here λ > 0 is known as the Frank-Kamenetskii parameter. In [15,16], Liang and Wang studied the classification and evolution of bifurcation curves of positive solutions for the one-dimensional perturbed Gelfand equation with Dirichlet-Neumann boundary conditions given by…”

“…where 4 ≤ a < ∞. They proved that the shape of the bifurcation curve depended on the value of a, c. The proofs given in [15,16] are more subtle and complicated. The results substantially improve and generalize those given in [10].…”

“…In [10], Hung, Wang and Yu gave rigorous theoretical proofs of some computational results of [6]. In [15,16], Liang and Wang gave more perfect results on (1.5). Notice that these results are all on exponential nonlinearity.…”