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MULTIPLICITY OF POSITIVE SOLUTIONS TO SCHRÖDINGER-TYPE POSITONE PROBLEMS

  • Ko, Eunkyung (Major in Mathematics, College of Natural Science, Keimyung University)
  • Received : 2021.12.24
  • Accepted : 2022.01.03
  • Published : 2022.01.31

Abstract

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝN, N > 2, λ is a positive parameter, V ∈ L(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

Keywords

Acknowledgement

This work was financially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2020R1F1A1A01065912).

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