Existence And Regularity Of Solutions For A Nonlinear Elliptic Equation With Dirichlet-Boundary

In this paper, we analyze weak solutions to the Dirichlet-boundary problem of a nonlinear elliptic equation involving the p-Laplacian:We perform the change of functionThe problem (1) becomes problem (2) which is a Dirichlet boundary problem of a quasilinear elliptic equation involving the p-Laplacian: Then, we study existence and regularity results of weak solutions to problem (2) according with the variational principle. Moreover, we also study a nonexistence result of weak solutions to problem (1).