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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.5
- 수록면
- 298 - 306 (9page)
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We investigate the existence of multiple positive solutions of the following elliptic equation with a Schr\"odinger-type term:$$\,\,\,\,\,\,\,\,\,\,\,\,\left\{\begin{array}{rlll}-\Delta u +V(x) u&=&\lambda f(u) & x \in\Omega,\\u &=&0, & x \in \partial\Omega,\end{array}\right.
$$where $0 \in \Omega$ is a bounded domain in $ \mathbb{R}^N, N\geq 1,$ with a smooth boundary $\partial\Omega,$$f \in C [0,\infty)$, $V \in L^\infty (\Omega) $ and$\lambda$ is a positive parameter. In particular, when $f (s) >0 $ for $ 0 \leq s < \sigma $ and $f(s) <0$ for $s > \sigma,$ we establish the existence of at least three positive solutions for a certain range of $\lambda$ byusing the method of sub and supersolutions.
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