Bifurcation and multiplicity results for a class of <inline-formula><tex-math id="M1">\begin{document}$n\times n$\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$p$\end{document}</tex-math></inline-formula>-Laplacian system
Bifurcation and multiplicity results for a class of <inline-formula><tex-math id="M1">\begin{document}$n\times n$\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$p$\end{document}</tex-math></inline-formula>-Laplacian system
In this paper we study the positive solutions to the $n\times n$ $p$-Laplacian system:\begin{document}$\begin{equation*}\begin{cases}-\left(\varphi_{p_1}(u_1')\right)' = \lambda h_1(t) \left(u_1^{p_1-1-\alpha_1}+f_1(u_2)\right),\quad t\in (0,1),\\-\left(\varphi_{p_2}(u_2')\right)' = \lambda h_2(t) \left(u_2^{p_2-1-\alpha_2}+f_2(u_3)\right),\quad t\in (0,1),\\\quad\quad\quad\vdots\qquad\,\: =\quad\quad\quad\quad\quad\quad \vdots\\-\left(\varphi_{p_n}(u_n')\right)' = \lambda h_n(t) \left(u_n^{p_n-1-\alpha_n}+f_n(u_1)\right),~~\, t\in (0,1),\\\quad\,\,\,\, u_j(0)=0=u_j(1); ~~ j=1,2,\dots,n, \\ \end{cases}\end{equation*}$\end{document}where $\lambda$ is a positive parameter, $p_j>1$, $\alpha_j\in(0,p_j-1)$, $\varphi_{p_j}(w)=|w|^{p_j-2}w$, and $h_j \in …