Some singular, nonlinear differential equations arising in boundary layer theory

Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term

“…For example, super-diffusivity equations of this type have been proposed by de Gennes [15] as a model for long range Van der Waals interactions in thin films spreading on solid surfaces. This equation also appears in the study of cellular automata and interacting particle systems with self-organized criticality (see [8]), as well as to describe the flow over an impermeable plate (see [5,6]). …”

On similarity solutions of MHD flow over a nonlinear stretching surface in non-Newtonian power-law fluid

“…On the base of numerical simulations for λ = 0, Steinheuer [18] and Klemp and Acrivos [16] reported that to the Blasius-equation dual solutions exist as long as λ is smaller than the critical value λ c , after which no similarity solutions exist. For λ < 0, Callegari and Nachman [7] proved the existence of unique solution. For n = 1, m = 0, M = 0 and 0 < λ < λ c the non-uniqueness of the solution was shown by Hussaini and Lakin [14] and λ c was found to be 0.3541.…”

Compatibility conditions for the existence of weak solutions to a singular elliptic equation

“…Author details 1 School of Mathematics, Jilin University, No. 2699 Qianjin Street, Changchun, 130012, P.R.…”