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Elliptic perturbations for Hammerstein equations with singular nonlinear term. (English) Zbl 1112.35013

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.

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
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