Journal of the
Korean Mathematical Society JKMS

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^{1}$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at $0$ and $\infty$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

Keywords: generalized Laplacian system, singular weight, multiplicity, positive solution

MSC numbers: 34B16, 34B18

Supported by: The first author was supported by the National Research Foundation of Korea, Grant funded by the Korea Government (MEST)(NRF 2016R1D1A1B04931741)