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We investigate a class of quasi-linear multi-point boundary value problem with one-dimensional p-Laplacian. By applying monotone iterative technique, some sufficient conditions for the existence of twin positive solutions are established, they are the maximal and minimal solutions of the above problem. At the same time, we also establish iterative schemes for approximating this twin solutions, which...
A multi region finite difference method is described and applied to the one dimension, semi linear, singularly perturbed boundary value problem (SPBVP). The process of developing high precision algorithms for this problem is described and it is shown that when the multi region method is combined with the use of these high order algorithms, numerical solutions can achieve accuracies in the range of...
In this paper, a new difference scheme by using cubic splines for solving a singularly-perturbed two-point boundary-value problem for second-order ordinary differential equations is derived. The proposed scheme is fourth order accurate, which is better than previous published results. Finally, two numerical examples are solved to illustrate the efficiency of our method.
In this paper, we consider a kind of boundary value problem of a second order elliptic differential equation of variable coefficient. First, we give the variation inequality which is equal to this boundary value problem, and prove the existence and uniqueness of the solution of the variation inequality of this kind by using Green formula and variation method lemma. Then we can obtain the existence...
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