Multiplicity results of positive solutions for singular generalized Laplacian systems
J. Korean Math. Soc. 2019 Vol. 56, No. 5, 1309-1331
Published 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
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