We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model isHere Ω is an open bounded subset of R N (N ≥ 2), ∆ p u := div(|∇u| p−2 ∇u) (1 < p < N ) is the p-laplacian operator, µ is a nonnegative bounded Radon measure on Ω and H(s) is a continuous, positive and finite function outside the origin which grows at most as s −γ , with γ ≥ 0, near zero.2010 Mathematics Subject Classification. 35J60, 35J61, 35J75, 35R06.
We consider existence and uniqueness of solutions to elliptic problems set in open subsets of
\mathbb R^N
, bounded and unbounded. These problems are characterised by the presence of a linear higher order term and a nonlinear lower order term which may blow up where the solution is zero and which involves a distribution.
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