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Positive solutions of sub-superlinear Sturm–Liouville problems

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  • Cheng, Xiyou
  • Dai, Guowei

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.

Suggested Citation

  • Cheng, Xiyou & Dai, Guowei, 2015. "Positive solutions of sub-superlinear Sturm–Liouville problems," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 351-359.
  • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:351-359
    DOI: 10.1016/j.amc.2015.03.125
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