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EnglishWe discuss the existence and the asymptotic behavior of positive radial solutions for the following equation: Δpu(x) + f (u, x) = 0, where Δpu = div(Dup-2Du), x ℝn, n > p > 1, and we assume that f ≥ 0 is subcritical for u large and x small and supercritical for u small and x large, with respect to the Sobolev critical exponent. We give sufficient conditions for the existence of ground states with fast decay. As a corollary we also prove the existence of ground states with slow decay and of singular ground states with fast and slow decays. For the proofs we use a Fowler transformation which enables us to use dynamical arguments. This approach allows to unify the study of different types of non-linearities and to complete the results already appeared in literature with the analysis of singular solutions.
| Titolo: | Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type. |
| Autori: | |
| Data di pubblicazione: | 2010 |
| Rivista: | |
| Abstract: | We discuss the existence and the asymptotic behavior of positive radial solutions for the following equation: Δpu(x) + f (u, x) = 0, where Δpu = div(Dup-2Du), x ℝn, n > p > 1, and we assume that f ≥ 0 is subcritical for u large and x small and supercritical for u small and x large, with respect to the Sobolev critical exponent. We give sufficient conditions for the existence of ground states with fast decay. As a corollary we also prove the existence of ground states with slow decay and of singular ground states with fast and slow decays. For the proofs we use a Fowler transformation which enables us to use dynamical arguments. This approach allows to unify the study of different types of non-linearities and to complete the results already appeared in literature with the analysis of singular solutions. |
| Handle: | http://hdl.handle.net/11566/39376 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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