Existence of Positive Solutions for Three-Point Boundary Value Problem with $p$-Laplacian
Received:December 24, 2004  Revised:April 29, 2005
Key Words: $p$-Laplacian   three-point boundary value problem   cone   Krasnoselskii's fixed-point theorem.  
Fund Project:the National Natural Science Foundation of China (10371006)
Author NameAffiliation
MA De-xiang Department of Mathematics and Physics, North China Electric Power University (Beijing), Beijing 102206, China 
GE Wei-gao Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China 
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Abstract:
      By means of the Krasnoselskii's fixed-point theorem in cone, we study the existence of positive solution for the three-point boundary value problem with $p$-Laplacian operator $$\left\{\begin{array}{ll}(\phi_p(u'(t)))'+a(t)f(u(t))=0,\;\;\;t\in (0,1),\\ u(0)=\alpha u(\eta),\;u(1)=\beta u(\eta), \end{array}\right.$$ where $0<\alpha,\; \beta< 1,$ $0<\eta< 1$ and $\phi_p(z)=|z|^{p-2}z,\; p>1.$ Sufficient conditions are given which guarantee the existence of positive solutions of this problem.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.02.029
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