Varying domains in a general class of sublinear elliptic problems
Southwest Texas State University, Department of Mathematics
In this paper we use the linear theory developed in  and  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  -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., )-.
Continuous dependence, Positive solutions, Sublineal elliptic problems, Varying domains, Maximum principle, Principal eigenvalue
Cano-Casanova, S., & Lopez-Gomez, J. (2004). Varying domains in a general class of sublinear elliptic problems. <i>Electronic Journal of Differential Equations, 2004</i>(74), pp. 1-41.