In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal...In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.展开更多
By mixed monotone method, we establish the existence and uniqueness of positive solutions for fourth-order nonlinear singular Sturm-Liouville problems. The theorems obtained are very general and complement previously ...By mixed monotone method, we establish the existence and uniqueness of positive solutions for fourth-order nonlinear singular Sturm-Liouville problems. The theorems obtained are very general and complement previously known results.展开更多
In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
文摘In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.
文摘By mixed monotone method, we establish the existence and uniqueness of positive solutions for fourth-order nonlinear singular Sturm-Liouville problems. The theorems obtained are very general and complement previously known results.
文摘In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
