Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of...Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the ＂height＂ of nonlinear term is appropriate on a bounded set.展开更多
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 ...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.展开更多
基金The Natural Science Foundation of Gansu Province (NoZS031-A25-003-Z)
文摘Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the ＂height＂ of nonlinear term is appropriate on a bounded set.
文摘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.
