On singularly weighted generalized Laplacian systems and their applications (Q1748281)

A \(\phi\)-Laplacian system with a possibly non-integrable weight is studied under homogeneous Dirichlet boundary conditions, namely: \[ -\phi(u')' = \lambda h(t) \cdot f(u), \] \[ u(0)=u(1)=0, \] where \(h:(0,1)\to \mathbb R_+^N\), \(f:\mathbb R_+\to \mathbb R_+^N\) and \(h \cdot f:= (h_1f_1,\ldots ,h_Nf_N)\). Under appropriate conditions on the assymptotic behavior of the involved functions, explicit intervals for existence and nonexistence of positive solutions are obtained.