SYSTEMS OF SINGULAR INTEGRAL EQUATIONS AND APPLICATIONS TO EXISTENCE OF REVERSED FLOW SOLUTIONS OF FALKNER-SKAN EQUATIONS

摘要

We investigate existence of reversed flow solutions of the Falkner-Skan equations by considering a system of two singular Hammerstein integral equations. We prove that the reversed flow solutions exist for each parameter in (-1/6,0). This is an extension of results on nonexistence of reversed flow solutions obtained recently by the authors. As applications of our new results,we obtain existence of reversed flow similarity solutions of the boundary layer equations governing the flow of fluids over surfaces often arising from engineering problems.