一类悬臂梁方程的可解性

Solvability of a Class of Cantilever Beam Equations

用锥上不动点定理,研究一类悬臂梁方程{w″″(t)=λf(t,w(t)),t∈(0,1),w(0)=w′(0)=w″(1)=w(1)=0,其中λ为正参数,f∈C([0,1]×[0,∞),[0,∞)).在非线性项f满足超线性或者次线性增长条件的情形下给出其正解的存在性和多解性结果.

By using the fixed point theorem on the cone,the author study a class of cantilever beam equations {w″″(t)=λf(t,w(t)),t∈(0,1),w(0)=w′(0)=w″(1)=w(1)=0,whereλis a positive parameter,f∈C([0,1]×[0,∞),[0,∞)).The existence and multiplicity results of its positive solutions are given when the nonlinear term f satisfies superlinear or sublinear growth condition.