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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.5
- 수록면
- 319 - 328 (10page)
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We establish an existence result for a positive solution to the Schr\"odinger-type singular semipositone problem:$-\Delta u+V(x)u=\lambda \frac{ f(u)}{u^\alpha}$ in $ \Omega, ~u=0 $ on $\partial \Omega,$where $\Omega$ is a bounded domain in $ \mathbb{R}^N, N >2, \lambda \in \mathbb{R}$ is a positive parameter,$V \in L^\infty(\Omega)$, $0< \alpha <1$, $ f \in C([0, \infty), \mathbb{R})$ with $f(0) <0$.
In particular, when $\frac{f(s)}{s^\alpha}$ is sublinear at infinity,% and the case when f satisfies sublinear growth condition,we establish the existence of a positive solutions for $\lambda \gg 1$. 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.
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