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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence results
for superlinear semipositone $\text{BVP}$'s


Authors: V. Anuradha, D. D. Hai and R. Shivaji
Journal: Proc. Amer. Math. Soc. 124 (1996), 757-763
MSC (1991): Primary 34B15
MathSciNet review: 1317029
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

V. Anuradha
Affiliation: Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72212

D. D. Hai
Email: dang@math.msstate.edu

R. Shivaji
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: shivaji@math.msstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03256-X
PII: S 0002-9939(96)03256-X
Received by editor(s): June 10, 1994
Additional Notes: The third author was partially supported by NSF Grants DMS-9215027. This author also thanks the CDSNS at Georgia Institute of Technology, Atlanta, GA, for providing a Visiting Research Scientist position (Fall 1993) during which time this work was completed
Communicated by: Hal Smith
Article copyright: © Copyright 1996 American Mathematical Society