Аннотация:We consider the Robin eigenvalue problem for the Laplace operator in a bounded domain
with a real parameter. We investigate
the behavior of the eigenvalues of this problem as functions of the parameter . We
analyze the monotonicity and convexity properties of the eigenvalues. We obtain estimates to the difference between the k-th eigenvalue of the Laplace
operator with Dirichlet boundary condition in
and the corresponding Robin eigenvalue
for positive values of for every k = 1, 2, . . ..