两端固定的奇异梁方程的多重正解

设 n 是一个任意的自然数. 证明了一个两端固定的奇异梁方程的 n 个正解的存在性, 其中非线性项是一个Carathéodory 函数. 主要工具是涉及非线性项的高度函数与锥压缩锥拉伸型的 Krasnoselskii不动点定理. 进一步的研究表明,如果非线性项在零点和无穷远处的增长极限均为无界函数, 该方程仍可能具有正解.

Multiple Positive Solutions to a Singular Beam Equation Fixed at Both Ends

Let n be an arbitrary natural number. The existence of n positive solutions is proved for a singular beam equation fixed at both ends, where the nonlinear term is a Caratheodory function. Main tools are height functions concerned with nonlinear term and Guo-Krasnoselskii fixed point theorem of cone expansion-compression type. Further research shows that the equation may have positive solution if the growth limits of nonlinear term at zero and infinity are unbounded functions.