Santiago Cano-Casanova

Varying boundary conditions in a general class of elliptic problems of mixed type

Abstract In this paper we use the linear theory developed in Cano-Casanova and Lopez-Gomez (J. Differential Equations 178 (2002) 123) 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 boundary operator. Besides working with mixed non-classical boundary conditions, this paper considers problems where bifurcation from infinity occurs. Treating this kind of problems is far from easy, since a complete knowledge of the set of values of the parameters where they exhibit a positive solution is imperative. Our results are far from immediate, as a consequence of the vanishing weight functions involved in our general setting. Now a days, the analysis of these general problems, where the coefficients are allowed to vary and eventually vanishing or changing sign, is focusing a great deal of attention.