A NECESSARY AND SUFFICIENT CONDITION FORSINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS

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摘要 Inthispaperthefollowingresultisobtained:Supposef(x.u,v)isnonnegative,con-tinuousin(a,b)×R^+×R^+;fmaybesingularatx=a(and/orx=b)andv=0;fisnonde-creasingonuforeachx,v,nonincreasingonv[oreachx.u;thereexistsaconstantq∈(0,1)suchthatt^qf(x,t^-1u,tu)≤f(x,u,u)≤λqf(x,λ^-1u,λu),V00,e(x)=G(x,x),G(x,y)isGreen'sfunctionofabovementionedboundaryvalueproblem(whenf(x,u,v)≡O).
机构地区 不详
出版日期 1998年01月11日(中国期刊网平台首次上网日期,不代表论文的发表时间)