Cano-Casanova, Santiago; López-Gómez, Julián Varying domains in a general class of sublinear elliptic problems. (English) Zbl 1109.35352 Electron. J. Differ. Equ. 2004, Paper No. 74, 41 p. (2004). In this paper we use the linear theory developed in our papers [J. Differ. Equations 178, No. 1, 123–211 (2002; Zbl 1086.35073) and Nonlinear Anal., Theory Methods Appl. 47, No. 3, 1797–1808 (2001; Zbl 1042.35600)] 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 E. N. Dancer and D. Daners [J. Differ. Equations 138, No. 1, 86–132 (1997; Zbl 0886.35063)] – 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.,the second author, Electron. J. Differ. Equ. 2000, Conf. 05, 135–171 (2000; Zbl 1055.35049)]). Cited in 3 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B50 Maximum principles in context of PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:Continuous dependence; positive solution; sublinear elliptic problems; varying domains; maximum principle; principal eigenvalue Citations:Zbl 1086.35073; Zbl 1042.35600; Zbl 0886.35063; Zbl 1055.35049 PDFBibTeX XMLCite \textit{S. Cano-Casanova} and \textit{J. López-Gómez}, Electron. J. Differ. Equ. 2004, Paper No. 74, 41 p. (2004; Zbl 1109.35352) Full Text: EuDML EMIS