Varying domains in a general class of sublinear elliptic problems

Cano-Casanova, Santiago
Lopez-Gomez, Julian
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Southwest Texas State University, Department of Mathematics
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])-.
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.