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1IntroductionInarecentsurveypaperTuckandSchwarts[3]discussedaseriesofthird-orderordinarydifferentialequationsarisinginthestudyoftheflowofathinfilmofviscousfluidoverasolidsurface.Whensuchafilmdrainsdownaverticalwallandtheeffectsofsurfacetensionandgravityaswellasviscosityaretakenintoaccount,oneisledtoanequationoftheformforthefilmprofiley(x)inacoordinateframemovingwiththefluid.Herethex--axisischosentobepointingupwords.Generallyspeaking,thefunctionf(y)issingularaty=0,thatis,atthetipofthefilm.Its… 相似文献
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(王俊禹)(郑大伟)(王学孔)ASINGULARORNONSINGULARPERTURBATIONPROBLEMFORASECONDORDERNONLINEARDIFFERENTIALEQUATIONWITHTWOFREEENDPOINTS¥Wang... 相似文献
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The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem. 相似文献
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王俊禹 《数学年刊B辑(英文版)》1991,(1)
This paper studies the boundary value problem involving a small parameter((k(V(t))+ε)[V'(s)[~(n-1V'(s))'+(sg(V(s))+f(V(s))V'(s)=0 for s∈R,V(-∞)=A,V(+∞)=B;A0,U(x,0)=A for x<0,U(x,0)=B for x>0,under the hypotheses H_1—H_4.The author's aim is not only to determine explicitly thediscontinuous solution U_0(x,t)=V_0(s),s=x/p(t),to the reduced problem,and the formand the number of its curves of discontinuity,but also to present,in an extremely naturalway,the jump conditions which it must satisfy on each of its curves of discontinuity.Itis proved that the problem has a unique solution U_ε(x,t)=V_ε(s),s=x/p(t),ε≥0,V_ε(s)pointwise converges to V_0(s)as ε 0,V_0(s)has at least one jump point if and only if k(y)possesses at least one interval of degeneracy in[A,B],and there exists a one-to-onecorrespondence between the collection of all intervals of degeneracytof k(y)in[A,B]andthe set of all jump points of V_0(s). 相似文献
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