一类具有两个固定端点的非线性弹性梁方程的可解性(英文)

Solvability of a Class of Nonlinear Elastic Beam Equations with Both Fixed Ends

利用Leray-Schauder非线性抉择对下列非线性项含有各阶导数的弹性梁方程建立了一个存在定理:u(4)(t)+f(t,u(t),u′(t),u″(t),u(t))=e(t),0≤t≤1,u(0)=u(1)=u′(0)=u′(1)=0.在材料力学中,该方程描述了两个端点固定的弹性梁的形变.我们的结论表明如果非线性项满足某种线性增长限制则该方程至少有一个解.

By applying Leray-Schauder Nonlinear Alternative, an existence theorem is established for the following elastic beam equation in which nonlinear term contains all order derivatives {u（4）（t） ＋ f（t,u（t）,u^1（t）,u^n（t）,u^w（t）） = e（t）,0≤ t ≤ 1,（0）=u（1）=u＇（0）=u＇（1）=0}In the material mechanics, the equation describes the deformation of an elastic beam whose both ends are fixed. Our results show that the equation has at least one solution provided the nonlinear term satisfies a linear growth restriction.