Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 74, pp. 1-41.

Title: Varying  domains in a general class
       of sublinear elliptic problems

Authors: Santiago Cano-Casanova (Univ. Pontificia Comillas de Madrid, Spain)
 Julian Lopez-Gomez (Univ. Complutense de Madrid, Spain)

Abstract:
 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.