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Unique existence results and numerical solutions for fourth-order impulsive differential equations with nonlinear boundary conditions
Hui Wang,Lingling Zhang,Xiaoqiang Wang
Keywords:Existence and uniqueness;impulsive differential equations;fixed point theorem for sum operator;numerical solution
Abstract:
      The work is concerned with three kinds of fourth-order impulsive differential equations with nonlinear boundary conditions. We at first focused on studying the existence and uniqueness of positive solutions for these kinds of problems. By converting the problem to an equivalent integral equation, then applying the new class of fixed point theorems for the sum operator on cone, we obtain the sufficient conditions which not only guarantee the existence of a unique positive solution, but also be applied to construct two iterative sequences for approximating it. Further, we present the numerical methods for solving the fourth-order differential equations. At last, some examples are given with numerical verifications to illustrate the main results.