Electron. J. Diff. Eqns., Vol. 2004(2004), No. 74, pp. 1-41.

Varying domains in a general class of sublinear elliptic problems

Santiago Cano-Casanova & Julian Lopez-Gomez

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.

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Santiago Cano-Casanova
Departamento de Matematica Aplicada y Computacion
Universidad Pontificia Comillas de Madrid
28015-Madrid, Spain
email: scano@dmc.icai.upco.es
Julian Lopez-Gomez
Departamento de Matematica Aplicada
Universidad Complutense de Madrid
28040-Madrid, Spain
email: Lopez_Gomez@mat.ucm.es

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