左端刚性固定右端简单支撑的奇异梁方程正解的存在性

设E0,1]是一个零测度的闭子集。对于左端刚性固定右端简单支撑的非线性梁方程u^（（4））（t）=f（t,u（t））,t∈0,1]／E,u（0）=u（1）=u′（0）=u″（1）=0,证明了一个新的正解存在定理,其中允许非线性项f（t,u）是非单调的并且在t=0,t=1及u=0处是奇异的.主要工具是全连续算子的逼近定理和锥压缩锥拉伸型的Guo-Krasnoselskii不动点原理。

Existence of Positive Solution to Singular Beam Equations Rigidly Fixed at Left and Simply Supported at Right

Let E 0,1]be a closed subset with zero measure.A new existence theorem of positive solution is proved for the nonlinear elastic beam equation rigidly fixed at the left and simply supported at the right,u(4)(t)=f(t,u(t)),t ∈0,1]\E,u(0)=u(1)=u'(0)=u"(1)=0,where the nonlinear term f(t,u) is allowed to be nonmonotonic and singular at t=0,t=1 and u=0.Main tools are the approximation theorem of completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type.