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Semilinear elliptic equations in unbounded domains of Rn

  • Patrizia Donato (a1), Lucia Migliaccio (a2) and Rosanna Schianchi (a2)

Synopsis

We study, in unbounded domains Ω⊂Rn, an elliptic semilinear problem with homogeneous boundary conditions. We assume that the nonlinear term f(x, u, Du) satisfies some condition of quadratic growth with respect to Du. We prove, in the framework of weighted Sobolev spaces, that, if and are respectively a subsolution and a supersolution of our problem, then there exists a least solution ū and a greatest solution û in the ordered interval and we obtain some multiplicity results.

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