Electron. J. Diff. Eqns., Vol. 2006(2006), No. 104, pp. 1-23.

Elliptic perturbations for Hammerstein equations with singular nonlinear term

Giuseppe Maria Coclite, Mario Michele Coclite

Abstract:
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.

Submitted July 3, 2006. Published September 8, 2006.
Math Subject Classifications: 35B25, 45E99, 45G10, 45L99, 47H14.
Key Words: Hammerstein integral equations; existence of positive solutions; singular nonlinear boundary value problems; singular elliptic perturbations.

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Giuseppe Maria Coclite
Dipartimento di Matematica
Universitá di Bari
via Orabona 4, 70125 Bari, Italy
email: coclitegm@dm.uniba.it
Mario Michele Coclite
Dipartimento di Matematica
Universitá di Bari
via Orabona 4, 70125 Bari, Italy
email: coclite@dm.uniba.it

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