Nonexistence results for a degenerate Goursat type Problem

For a generalization of the Gellerstedt operator with Dirichlet boundary conditions in a Tricomi domain. We establish Pohožaev-type identities and prove the nonexistence of nontrivial regular solutions. Furthermore, we investigate the critical exponent phenomenon for power-type nonlinearities, characterized by the critical exponent of a weighted Sobolev embedding.