## Positive solutions for an integro-differential equation with singular nonlinear term.(English)Zbl 1212.45013

Summary: The existence of a positive solution in a weighted Sobolev space for a homogeneous semilinear elliptic integro-differential Dirichlet problem is proved. The integral operator of the equation depends on a nonlinear function with a singularity at the origin.

### MSC:

 45K05 Integro-partial differential equations 45M20 Positive solutions of integral equations 45G05 Singular nonlinear integral equations