Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (2): 189-195.

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EXISTENCE RESULTS FOR SEMIPOSITONE BOUNDARY VALUE PROBLEMS

 WANG Ru-Fa, MA Ru-Yun, REN Li-Shun   

  1. Gansu Institute of political science and law, Lanzou 730070, China Department of Mathematics, Northwest Normal university, Lauzhou 730070, China Department of Mathematics, Zhoukou Teachers Collage, Zhoukou 466000
  • Online:2001-04-07 Published:2001-04-07

Abstract:

We study the existence of positive solutions to the boundary value problem (p(t)u′)′ + f(t, u) + e(t, u) = 0, r < t < R, au(r) − bp(r)u′(r) = 0, cu(R) + dp(R)u′(R) = 0,where f and e : [r,R] × [0,1) ! R are two continuous functions satisfying f  0 and |e|  M for some M > 0. We show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and  > 0 is small enough; (ii) f is sublinear at infinity and  > 0 is large enough. Our proofs are based on fixed point theorems in a cones.

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