East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR A SCHRÖDINGER-TYPE SINGULAR FALLING ZERO PROBLEM

  • Eunkyung Ko (Major in Mathematics, College of Natural Science, Keimyung University)
  • Received : 2023.04.11
  • Accepted : 2023.05.16
  • Published : 2023.05.31
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Abstract

Extending [14], we establish the existence of multiple positive solutions for a Schrödinger-type singular elliptic equation: $$\{{-{\Delta}u+V(x)u={\lambda}{\frac{f(u)}{u^{\beta}}},\;x{\in}{\Omega}, \atop u=0,\;x{\in}{\partial}{\Omega},$$ where 0 ∈ Ω is a bounded domain in ℝN, N ≥ 1, with a smooth boundary ∂Ω, β ∈ [0, 1), f ∈ C[0, ∞), V : Ω → ℝ is a bounded function and λ is a positive parameter. In particular, when f(s) > 0 on [0, σ) and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

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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