In this paper we are concerned with the solutions of the differential equation <i>f '''</i> + <i>ff ''</i> + <i>g</i>(<i>f '</i>) = 0 on [0,<FONT SIZE=+1 FACE='Symbol'>¥</FONT>), satisfying the boundary conditions <i>f</i>(0) = <FONT SIZE='3' FACE='Symbol'>a</FONT>, <i>f '</i>(0) = <FONT SIZE='3' FACE='Symbol'>b ³</FONT> 0, <i>f '</i>(<FONT SIZE=+1 FACE='Symbol'>¥</FONT>) = <FONT SIZE=+1 FACE='Symbol'>l</FONT>, and where <i>g</i> is some given continuous function.This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent to stretching walls in the context of boundary layer approximation.Under some assumptions on the function <i>g</i>, we prove existence and uniqueness of a concave or a convex solution. We also give some results about nonexistence and asymptotic behaviour of the solution.
Uitgever:
Acta Mathematica Universitatis Comenianae, Institute of Applied Mathematics (provided by DOAJ)
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