An Elliptic singular problem with a nonlocal boundary condition

P. AMSTER; M. MAURETTE

JOURNAL OF NONLINEAR ANALYSIS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2012 vol. 75 p. 5815 - 5823

0362-546X

We study the existence of solutions for the nonlinear elliptic system $Delta u+g(u)=f(x)$, where $gin C(mathbb R^Nackslash S,mathbb R^N$) with $Ssubset R^N$ bounded. Using topological degree methods, we prove an existence result under a geometric condition on $g$. Moreover, we analyze the particular case of an isolated repulsive singularity: under a Nirenberg type condition, we prove the existence of a sequence of solutions of appropriate approximated problems that converges to a generalized solution.