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Existence results for superlinear semipositone 's

Authors:	V Anuradha D D Hai R Shivaji

Institution:	Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72212 D. D. Hai ; Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762 ; Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762

Abstract:	We consider the existence of positive solutions to the BVP $\begin{gather}(p(t)u')' + \lambda f(t,u)=0,\qquad r<t<R, au(r)-bp(r)u'(r)=0, cu(R) +dp(R)u'(R)=0, \end{gather}$ where $\lambda>0$ . Our results extend some of the existing literature on superlinear semipositone problems and singular BVPs. Our proofs are quite simple and are based on fixed point theorems in a cone.

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