Positive solutions of sub-superlinear Sturm–Liouville problems

Xiyou Cheng and Guowei Dai

Applied Mathematics and Computation, 2015, vol. 261, issue C, 351-359

Abstract: In this paper, we introduce the notion of a strict lower/upper solution to nonlinear Sturm–Liouville boundary value problems. Based on the maximum principles, we establish a result of Leray–Schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions. Applying the result and the fixed point index theory in cones, we obtain the global existence results of positive solutions for sub-superlinear Sturm–Liouville problems.

Keywords: Positive solution; Nonlinear eigenvalue problem; Strict lower and upper solutions; Leray–Schauder degree; Fixed point index (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:351-359

DOI: 10.1016/j.amc.2015.03.125

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