A Weighted Problem for p-Laplacian Discussed with a Result of Saddle Point Type

Weighted problems for the p-Laplacian represent a wide range of models arising from real-world research. Solving such problems involves, in many situations, variational approaches that are various and a virtually inexhaustible resource. In this paper, starting from a weakened saddle point type result, an existence theorem for a special kind of Dirichlet weighted problem involving the p-Laplacian is proved using a broad range of additional results. The continuing importance of this type of result is supported by a discussion on the applicability of the model as well as by the possibility of constructing a concrete solution via an appropriate numerical method based on saddle point–type results.