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本文研究下述Sturm-Liouville边值问题利用Schauder不动点定理、上下解方法和Leray-Schauder映射度理论,获得了解的非存在性、存在性和多重性结果.其中一些是全新的结果,另一些则扩展、改进和完善了由Erbe,Wang,Hai,Lee和Lin所获得的结果.  相似文献   
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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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王俊禹  高文杰 《东北数学》2005,21(2):158-164
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  高文杰 《东北数学》1996,12(3):307-312
奇异两点边值问题正解的存在性@王俟禹@高文杰...  相似文献   
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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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本文研究一个主部为N维P-Laplace微分算子的非线性偏微分方程的边值问题.方程中的非线性项关于其变量可以具有奇性和间断性.这类方程的一种典型情形是大家熟知的具负指数的Emden-Fowler方程.本文利用摄动技巧,Schauder不动点定理,经对解的性质的精细分析.获得了解的存在性和唯一性结果.  相似文献   
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