Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 74, pp. 1-41.
Title: Varying domains in a general class
of sublinear elliptic problems
Authors: Santiago Cano-Casanova (Univ. Pontificia Comillas de Madrid, Spain)
Julian Lopez-Gomez (Univ. Complutense de Madrid, Spain)
Abstract:
In this paper we use the linear theory developed in [8]
and [9] to show the continuous dependence of the positive
solutions of a general class of sublinear elliptic boundary value
problems of mixed type with respect to the underlying domain. Our
main theorem completes the results of Daners and Dancer [12]
-and the references there in-, where the classical Robin
problem was dealt with. Besides the fact that we are working
with mixed non-classical boundary conditions, it must
be mentioned that this paper is considering problems where
bifurcation from infinity occurs; now a days, analyzing these
general problems, where the coefficients are allowed to vary and
eventually vanishing or changing sign, is focusing a great deal
of attention -as they give rise to metasolutions (e.g., [20])-.
Submitted April 20, 2004. Published May 21, 2004.
Math Subject Classifications: 35J25, 35J65, 58J37, 35B50, 35P30.
Key Words: Continuous dependence; positive solution;
sublineal elliptic problems; varying domains;
maximum principle; principal eigenvalue.