Existence of solutions to nonlocal and singular variational elliptic inequality via Galerkin method
F. J. S. A. Correa, UFPa, Belém, Brasil E. J. Qualitative Theory of Diff. Equ., No. 18. (2005), pp. 1-12.
S. B. Menezes, UFPa, Belém, Brasil
| Communicated by T. A. Burton. | Received on 2004-12-12 Appeared on 2005-08-30 |
Abstract: In this article, we study the existence of solutions for nonlocal variational elliptic inequality
$$ -M(\|u\|^2)\Delta u \geq f(x,u) $$
Making use of the penalized method and Galerkin approximations, we establish existence theorems for both cases when $M$ is continuous and when $M$ is discontinuous.
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