Electron. J. Diff. Eqns., Vol. 2004(2004), No. 143, pp. 1-8.

Twin positive solutions for fourth-order two-point boundary-value problems with sign changing nonlinearities

Yu Tian, Weigao Ge

Abstract:
A new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions to
$$\displaylines{ (\Phi_p(y''(t))''-a(t)f(t,y(t),y''(t))=0,\quad 0 less than t less than 1,\cr y(0)=y(1)=0=y''(0)=y''(1), }$$
where $f:[0,1]\times[0,\infty)\times(-\infty,0]\to R, a\in L^1([0,1],(0,\infty)) $. We also give some examples to illustrate our results.

Submitted August 28, 2004. Published December 3, 2004.
Math Subject Classifications: 34B10, 34B15.
Key Words: Fourth-order two-point boundary-value problem; fixed point theorem; double cones; positive solution.

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Yu Tian
Department of Applied Mathematics
Beijing Institute of Technology, Beijing 100081, China
email: tianyu2992@163.com
  Weigao Ge
Department of Applied Mathematics
Beijing Institute of Technology, Beijing 100081, China
email: gew@bit.edu.cn

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