Korean J. Math. Vol. 25 No. 1 (2017) pp.37-43
DOI: https://doi.org/10.11568/kjm.2017.25.1.37

Positive solutions of superlinear and sublinear boundary value problems

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Published: Mar 30, 2017
Keywords:
Boundary Value Problem, Superlinear, Sublinear, Cone, Compact map, Fixed Point Theory.
Mathematics Subject Classification:
34B15, 34B18, 47H10.

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Juan A. Gatica
Department of Mathematics University of Iowa Iowa City, IA 52242, USA
Yun-Ho Kim
Department of Mathematics Education Sangmyung University Seoul 110-743, Republic of Korea

Abstract

We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.


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References

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