Geodesic
Varying domains in a general class of sublinear elliptic problems
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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])-.
Classification : 35J25, 35J65, 58J37, 35B50, 35P30
Keywords: continuous dependence, positive solution, sublineal elliptic problems, varying domains, maximum principle, principal eigenvalue 
@article{EJDE_2004__2004__a6,
     author = {Cano-Casanova, Santiago and L\'opez-G\'omez, Juli\'an},
     title = {Varying domains in a general class of sublinear elliptic problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a6/}
}
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Cano-Casanova, Santiago; López-Gómez, Julián. Varying domains in a general class of sublinear elliptic problems. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a6/