Abstract
We consider the existence and multiplicity of positive solutions to the quasilinear system $$ \begin{cases} -\Delta_{p_{i}}u_{i} = \mu_{i}a_{i}(x)f_{i}(u_{1},\dots,u_{n})~\text{in}~\Omega,\;i=1,\dots,n, \\[1pt] u_{i} = 0~\text{on}~\partial \Omega , \end{cases} $$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ with a smooth boundary $\partial \Omega$, $\Delta_{p_{i}}u_{i}={\rm div}(|\nabla u_{i}|^{p_{i}-2}\nabla u_{i})$, $p_{i}>1$, $\mu_{i}$ are positive parameters, and $f_{i}$ are allowed to change sign.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.