Yao Qing-Liu
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China.
J Zhejiang Univ Sci. 2004 Mar;5(3):353-7. doi: 10.1007/BF02841022.
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the "height" of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
利用勒雷 - 绍德尔不动点定理、等价范数以及积分方程组技巧，建立了一类含二阶导数的非线性四阶两点边值问题的若干存在性定理。我们结果的主要条件是局部性的。换句话说，解的存在性可通过考虑有界集上非线性项的“高度”来确定。这类问题通常描述两端简支的弹性梁的平衡状态。
