International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 5, Pages 279-283
doi:10.1155/S0161171202007147
On the continuity of principal eigenvalues for boundary value problems with indefinite weight function with respect to radius of balls in ℝN
Ghasem Alizadeh Afrouzi
Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
Abstract
We investigate the continuity of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem −Δu(x)=λg(x)u(x), x∈BR(0);u(x)=0, |x|=R, where BR(0) is a ball in ℝN, and g is a smooth function, and we show that λ1+(R) and λ1−(R) are continuous functions of R.