20.500.12556/DiRROS-18198 Nodal solutions for Neumann systems with gradient dependence We consider the following convective Neumann systems: $\begin{equation*}\left(\mathrm{S}\right)\qquad\left\{\begin{array}{ll}-\Delta_{p_1}u_1+\frac{|\nabla u_1|^{p_1}}{u_1+\delta_1}=f_1(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega,\\ -\Delta _{p_2}u_2+\frac{|\nabla u_2|^{p_2}}{u_2+\delta_2}=f_2(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega, \\ |\nabla u_1|^{p_1-2}\frac{\partial u_1}{\partial \eta }=0=|\nabla u_2|^{p_2-2}\frac{\partial u_2}{\partial \eta} \text{on}\;\partial\,\Omega,\end{array}\right.\end{equation*}$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ ($N\geq 2$) with a smooth boundary $\partial\,\Omega, \delta_1, \delta_2 > 0$ are small parameters, $\eta$ is the outward unit vector normal to $\partial\,\Omega, f_1, f_2: \Omega \times \mathbb{R}^2 \times \mathbb{R}^{2N} \rightarrow \mathbb{R}$ are Carathéodory functions that satisfy certain growth conditions, and $\Delta _{p_i}$ ($1< p_i < N,$ for $i=1,2$) are the $p$-Laplace operators $\Delta _{p_i}u_i=\mathrm{div}(|\nabla u_i|^{p_i-2}\nabla u_i)$, for $u_i \in W^{1,p_i}(\Omega).$ In order to prove the existence of solutions to such systems, we use a sub-supersolution method. We also obtain nodal solutions by constructing appropriate sub-solution and super-solution pairs. To the best of our knowledge, such systems have not been studied yet. Neumann elliptic systems gradient dependence subsolution method supersolution method nodal solutions true false true Angleški jezik Ni določen Neznano 2024-02-16 13:21:22 2024-02-16 13:21:22 2024-02-19 13:37:55 0000-00-00 00:00:00 2024 0 0 19 str. article no. 4 Vol. 2024 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 517.9 1687-2770 10.1186/s13661-023-01814-2 180215555 https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-023-01814-2 1 8621df8a-ccbd-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24713 s13661-023-01814-2.pdf s13661-023-01814-2.pdf 1 0B6F5CF615DF90828E822E1CBBE3355D 01927d0df76550148b0b3bc0eeb713adfa3ac370e984109595388d1ee4c5ddce ae8ffdfe-ccbd-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24714 Inštitut za matematiko, fiziko in mehaniko 0 0 0