Problème de Dirichlet relatif à une perturbation non lineaire des espaces harmoniques

In this paper, we prove for a more general semi-linear perturbation of linear harmonic spaces, the existence and the unicity of the solution of the Dirichlet problem and we apply our results for the non-linear stationary Schrödinger equation.     

On the Existence of Positive Eigenvalues for Linear and Nonlinear Equations with Indefinite Weight

We prove the existence of positive eigenvalues for two types of equations having an indefinite weight. We consider the linear case, and we show the existence of a positive principal eigenvalue corresponding to a positive eigenfunction. For the nonlinear case, we show that the set of positive eigenvalues is an unbounded interval, and that the corresponding eigenfunctions are positive.     

Principal eigenvalues for indefinite weight problems in all of

We show the existence of principal eigenvalues of the problem in where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction at .