Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MULTIPLE SYMMETRIC POSITIVE SOLUTIONS OF A NEW KIND STURM-LIOUVILLE-LIKE BOUNDARY VALUE PROBLEM WITH ONE DIMENSIONAL p-LAPLACIAN

  • Zhao, Junfang (Department of Mathematics, Beijing Institute of Technology) ;
  • Ge, Weigao (Department of Mathematics, Beijing Institute of Technology)
  • Published : 2009.09.30
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Abstract

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

Keywords

References

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