Coclite, Giuseppe Maria; Coclite, Mario Michele Elliptic perturbations for Hammerstein equations with singular nonlinear term. (English) Zbl 1112.35013 Electron. J. Differ. Equ. 2006, Paper No. 104, 23 p. (2006). Summary: We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the integral equation are proved. Moreover, these results are applied to nonlinear singular homogeneous Dirichlet problems. Cited in 5 Documents MSC: 35B25 Singular perturbations in context of PDEs 45E99 Singular integral equations 45G10 Other nonlinear integral equations 35J25 Boundary value problems for second-order elliptic equations 47H14 Perturbations of nonlinear operators Keywords:existence of positive solutions; singular nonlinear boundary value problems; singular elliptic perturbations PDFBibTeX XMLCite \textit{G. M. Coclite} and \textit{M. M. Coclite}, Electron. J. Differ. Equ. 2006, Paper No. 104, 23 p. (2006; Zbl 1112.35013) Full Text: EuDML EMIS