East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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MULTIPLICITY OF POSITIVE SOLUTIONS OF A SCHRÖDINGER-TYPE ELLIPTIC EQUATION

  • Eunkyung Ko (Major in Mathematics, College of Natural Science, Keimyung University)
  • Received : 2024.01.23
  • Accepted : 2024.02.27
  • Published : 2024.05.31
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Abstract

We investigate the existence of multiple positive solutions of the following elliptic equation with a Schrödinger-type term: $$\begin{cases}-{\Delta}u+V(x)u={\lambda}f(u){\quad} x{\in}{\Omega},\\{\qquad}{\qquad}{\quad}u=0, {\qquad}\;x{\in}\partial{\Omega},\end{cases}$$, where 0 ∈ Ω is a bounded domain in ℝN , N ≥ 1, with a smooth boundary ∂Ω, f ∈ C[0, ∞), V ∈ L∞(Ω) and λ is a positive parameter. In particular, when f(s) > 0 for 0 ≤ s < 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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