Liouville type theorems for \(\varphi\)-subharmonic functions. (English) Zbl 1043.58022
Summary: We present some Liouville type theorems for solutions of differential inequalities involving the \(\varphi\)-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the \(p\)-Laplacian, and are new even in these cases. Phragmen-Lindelöff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
MSC:
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
| 31B05 | Harmonic, subharmonic, superharmonic functions in higher dimensions |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 35B50 | Maximum principles in context of PDEs |
