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Zbl 0857.34032
Anuradha, V.; Hai, D.D.; Shivaji, R.
Existence results for superlinear semipositone BVP's.
(English)
[J] Proc. Am. Math. Soc. 124, No.3, 757-763 (1996). ISSN 0002-9939; ISSN 1088-6826/e

The authors consider the existence of a positive solution to the Sturm-Liouville boundary value problem $(p(t)\cdot u')'+\lambda\cdot f(t,u)=0$, $r<t<R$, $a\cdot u(r)-b\cdot u'(r)=0$, $c\cdot u(R)+d\cdot u'(R)=0$, for $\lambda>0$ small under the condition $$\lim_{u\to\infty} {{f(t,u)}\over u}=\infty$$ uniformly on a compact subinterval of $(r,R)$. The main results of the paper are related to the cases: $f$ is a positive possibly singular function, and $f$ is a regular optionally positive function. The proofs of the results are based on fixed point theorems in a cone.
[A.Burmistrova (Chelyabinsk)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
34B24 Sturm-Liouville theory

Keywords: positive solution; Sturm-Liouville boundary value problem; fixed point theorems in a cone

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