Large solutions to an anisotropic quasilinear elliptic problem
In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem, in a bounded domain Ω ⊂ ℝN × ℝM, together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a soluti...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
| Aporte de: |
| Sumario: | In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem, in a bounded domain Ω ⊂ ℝN × ℝM, together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a solution, to this problem is r > max{p-1, q-1}. Assuming that r > q-1 ≥ p-1 > 0 we will show that the exponent q controls the blow-up rates near the boundary in the sense that all points of ∂Ω share the same profile, that depends on q and r but not on p, with the sole exception of the vertical points (where the exponent p plays a role). © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. |
|---|