We present several results on exact controllability for linear and nonlinear parabolic equations, both when the distributed control is acting linearly or nonlinearly on the whole domain. As a very particular case, we extend some recent works by means of a simpler constructive approach....

We study a symmetric nonlinear eigenvalue problem arising in earthquake initiation and we establish the existence of infinitely many solutions. Under the effect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with...