The existence of positive solution for singular Kirchhoff equation with two parameters
Abstract In this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω. $$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)+\mu h(x) \quad \mbox{in } \varOm...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-02-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1154-8 |
| Summary: | Abstract In this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω. $$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)+\mu h(x) \quad \mbox{in } \varOmega, \\ u>0 \quad \mbox{in } \varOmega, \\ u=0 \quad \mbox{on } \partial\varOmega. \end{cases} $$ By using the sub-supersolution method together with the comparison principle for elliptic equations, we obtain several existence and nonexistence theorems. Our works improve the results in the previous literature. |
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| ISSN: | 1687-2770 |