Browsing by Author "García-Melián, J"

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    Boundary blow-up solutions to elliptic systems of competitive type
    (2004) García-Melián, J; Rossi, JD
    We consider the elliptic system Deltau = u(p)v(q), Deltav = u(r)v(s) in Ohm, where p, s > 1, q, r > 0, and Ohm subset of R-N is a smooth bounded domain, subject to different types of Dirichlet boundary conditions: (F) u = lambda, v = mu, (I) u = v = +infinity and (SF) u = +infinity, v = mu on partial derivativeOhm, where lambda, mu > 0. Under several hypotheses on the parameters p, q, r, s, we show existence and nonexistence of positive solutions, uniqueness and nonuniqueness. We further provide the exact asymptotic behaviour of the solutions and their normal derivatives near partial derivativeOhm. Some more general related problems are also studied. (C) 2004 Published by Elsevier Inc.
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    On an elliptic problem with boundary blow-up and a singular weight
    (2003) Chuaqui, M; Cortázar, C; Elgueta, M; Flores, C; Letelier, R; García-Melián, J
    In this work we consider the non-autonomous problem Deltau = a(x)u(m) in the unit ball B subset of R-N, with the boundary condition u\(partial derivativeB) = +infinity, and m > 0. Assuming that a is a continuous radial function with a(x) similar to C-0 dist(x, partial derivativeB)(-gamma) as dist(x, partial derivativeB) --> 0, for some C-0 > 0, gamma > 0, we completely determine the issues of existence, multiplicity and behaviour near the boundary for radial positive solutions, in terms of the values of m and gamma. The case 0 < m less than or equal to 1, as well as estimates for solutions to the linear problem m = 1, are a significant part of our results.