East Asian mathematical journal

  • 제40권3호
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  • Pages.319-328
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  • 2024
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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EXISTENCE OF A POSITIVE SOLUTION TO INFINITE SEMIPOSITONE PROBLEMS

  • Eunkyung Ko (Major in Mathematics, College of Natural Science, Keimyung University)
  • 투고 : 2024.02.02
  • 심사 : 2024.05.01
  • 발행 : 2024.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

We establish an existence result for a positive solution to the Schrödinger-type singular semipositone problem: $-{\Delta}u\,=\,V(x)u\,=\,{\lambda}{\frac{f(u)}{u^{\alpha}}}$ in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝN , N > 2, λ ∈ ℝ is a positive parameter, V ∈ L∞(Ω), 0 < α < 1, f ∈ C([0, ∞), ℝ) with f(0) < 0. In particular, when ${\frac{f(s)}{s^{\alpha}}}$ is sublinear at infinity, we establish the existence of a positive solutions for λ ≫ 1. The proofs are mainly based on the sub and supersolution method. Further, we extend our existence result to infinite semipositone problems with mixed boundary conditions.

키워드

과제정보

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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