| Existence of Solutions to a Class of Higher-Order Singular Boundary Value Problem for One-Dimensional $p$-Laplacian |
| Received:July 12, 2005 Revised:January 20, 2006 |
| Key Words:
singular higher-order differential equation positive solution Vitali's convergence theorem.
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| Fund Project:the National Natural Science Foundation of China (10371006); the Foundation for PHD Specialities of Educational Department of China (20050007011). |
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| Abstract: |
| This paper deals with the existence of positive solutions for the problem $$\left\{\begin{array}{ll} (\Phi_p(x^{(n-1)}(t)))'+f(t, x, \ldots, x^{(n-1)})=0,\,\,\,\, 01.$ $f$ may be singular at $x^{(i)}=0, i=0, \ldots, n-2$. The proof is based on the Leray-Schauder degree and Vitali's convergence theorem. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.02.008 |
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