Multiplicity of Positive Solutions to Schr\"odinger-type Positone Problems
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We establish multiplicity results for positive solutions to the Schr\"odinger-type singular positone problem:$-\Delta u+V(x)u=\lambda f(u)$ in $ \Omega, ~u=0 $ on $\partial \Omega,$where $\Omega$ is a bounded domain in $ \mathbb{R}^N, N >2, \lambda$ is a positive parameter,$V \in L^\infty(\Omega)$ and $f:[0, \infty) \rightarrow (0, \infty)$ is a continuous function. In particular, when $f$ is sublinear at infinitywe discuss the existence of at least three positive solutions for a certain range of $\lambda$. The proofs are mainly based on the sub- and supersolution method.
Abstract
We establish multiplicity results for positive solutions to the Schr\"odinger-type singular positone problem:$-\Delta u+V(x)u=\lambda f(u)$ in $ \Omega, ~u=0 $ on $\partial \Omega,$where $\Omega$ is a bounded domain in $ \mathbb{R}^N, N >2, \lambda$ is a positive parameter,$V \in L^\infty(\Omega)$ and $f:[0, \infty) \rightarrow (0, \infty)$ is a continuous function. In particular, when $f$ is sublinear at infinitywe discuss the existence of at least three positive solutions for a certain range of $\lambda$. The proofs are mainly based on the sub- and supersolution method.
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