Generalized dirichlet problem in nonlinear potential theory.
We consider the eigenvalue problemin the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all are eigenvalues.
We consider the eigenvalue problem in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all λ > 0 are eigenvalues.
The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.