| RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY |
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| 作者姓名： | 田玉 葛渭高 |
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| 作者单位： | School of Science Beijing University of Posts and Telecommunications，Beijing 100876，China，Department of Applied Mathematics，Beijing Institute of Technology，Beijing 100081，China |
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| 基金项目： | Supported by National Natural Sciences Foundation of China(10371006)
Foundation for PhD Specialities of Educational Department of China(20050007011). |
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| 摘 要： | This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p 1,…, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t,x0,x1,…,xn-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.
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RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY |
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| Tian Yu School of Science,Beijing University of Posts and Telecommunications,Beijing ,China Ge Weigao.RIGHT FOCAL BOUNDARY VALUE PROBLEM WITH SINGULARITY[J].Acta Mathematica Scientia,2006(Z1). |
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| Authors: | Tian Yu School of Science Beijing University of Posts and Telecommunications Beijing China Ge Weigao |
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| Institution: | Tian Yu School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China Ge Weigao Department of Applied Mathematics,Beijing Institute of Technology,Beijing 100081,China |
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| Abstract: | |
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| Keywords: | Right focal Singular higher-order differential equation Regularization Vi-tali's convergence theorem |
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