Nodal solutions for Neumann systems with gradient dependence
Nodal solutions for Neumann systems with gradient dependence
Abstract We consider the following convective Neumann systems: $$ ( \mathrm{S} ) \quad \textstyle\begin{cases} -\Delta _{p_{1}}u_{1}+ \frac{ \vert \nabla u_{1} \vert ^{p_{1}}}{u_{1}+\delta _{1} }=f_{1}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in } \Omega , \\ -\Delta _{p_{2}}u_{2}+ \frac{ \vert \nabla u_{2} \vert ^{p_{2}}}{u_{2}+\delta _{2} }=f_{2}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in } \Omega …