Role of weight functions in the study of a Dirichlet problem concerning the Laplace problem with parameter spectral and non-homogeneous in a cone

In this work, we study the problem governed by the Laplacian operator perturbed by a spectral parameter and affected by a weight function in a cone. First, the study will be done in a space sector. We will show a theorem that links the study of this problem .This study is it provides original results in a richer functional space, more it covers the classical case.