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 Multiplicity results of positive solutions for singular generalized Laplacian systems J. Korean Math. Soc. 2019 Vol. 56, No. 5, 1309-1331 https://doi.org/10.4134/JKMS.j180658Published online September 1, 2019 Yong-Hoon Lee, Xianghui Xu Pusan National University; Ludong University Abstract : 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 Downloads: Full-text PDF   Full-text HTML