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    Electronic Resource
    Electronic Resource
    On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions (1995)
    Springer
    Probability theory and related fields 101 (1995), S. 251-276 
    Details
    ISSN: 1432-2064
    Keywords: 35J65 ; 60J65 ; 53C21
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in unbounded Lipschitz domainsD ⊂ ℝ d (d≥3), having compact boundary, with nonlinear Neumann boundary conditions on the boundary ofD. For this we use an implicit probabilistic representation, Schauder's fixed point theorem, and a recently proved Sobolev inequality forW 1,2(D). Special cases include equations arising from the study of pattern formation in various models in mathematical biology and from problems in geometry concerning the conformal deformation of metrics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01375828
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