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Semilinear Elliptic Problems in Unbounded Domains: Solutions in Weighted Sobolev Spaces

The semilinear elliptic equation Lu = f(x; u) in an unbounded domain IR N is studied. We use several embedding theorems of weighted Sobolev spaces to prove the solvability of this equation under natural growth conditions on f and on the coeecients of the elliptic operator L. This paper gives a uniied approach to such problems and generalizes some results in 1], 9] and 13].