This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
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
A free-boundary model of nonlinear dynamic system for pure forest is presented, in which the felling rate is unbounded nearby the free boundary. The effiect of unbounded function on a priori estimate and analysis of r...A free-boundary model of nonlinear dynamic system for pure forest is presented, in which the felling rate is unbounded nearby the free boundary. The effiect of unbounded function on a priori estimate and analysis of regularity is overcome, and the existence and uniqueness of the global classical solution to this system are proved.展开更多
基金Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China.
文摘This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
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.
基金Supported by the National Natural Science Foundation of China (90410011)
文摘A free-boundary model of nonlinear dynamic system for pure forest is presented, in which the felling rate is unbounded nearby the free boundary. The effiect of unbounded function on a priori estimate and analysis of regularity is overcome, and the existence and uniqueness of the global classical solution to this system are proved.
