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EnglishWe look for nonconstant, positive, radial, radially nondecreasing solutions of the quasilinear equation $-\Delta_p u+u^{p-1}=f(u)$ with $p>2$, in the unit ball $B$ of $\mathbb R^N$, subject to homogeneous Neumann boundary conditions. The assumptions on the nonlinearity f are very mild and allow it to be possibly supercritical in the sense of Sobolev embeddings. The main tools used are the truncation method and a mountain pass-type argument. In the pure power case, i.e., $f(u)=u^{q-1}$, we detect the limit profile of the solutions of the problems as $q\to\infty$. These results are proved in [3], in collaboration with B. Noris.
| Titolo: | A p-Laplacian Neumann problem with a possibly supercritical nonlinearity | |
| Autore/i: | F. Colasuonno | |
| Autore/i Unibo: | ||
| Anno: | 2016 | |
| Rivista: | ||
| Titolo del libro: | Bruxelles-Torino Talks in PDE’s Turin, May 2–5, 2016 | |
| Pagina iniziale: | 113 | |
| Pagina finale: | 122 | |
| Abstract: | We look for nonconstant, positive, radial, radially nondecreasing solutions of the quasilinear equation $-\Delta_p u+u^{p-1}=f(u)$ with $p>2$, in the unit ball $B$ of $\mathbb R^N$, subject to homogeneous Neumann boundary conditions. The assumptions on the nonlinearity f are very mild and allow it to be possibly supercritical in the sense of Sobolev embeddings. The main tools used are the truncation method and a mountain pass-type argument. In the pure power case, i.e., $f(u)=u^{q-1}$, we detect the limit profile of the solutions of the problems as $q\to\infty$. These results are proved in [3], in collaboration with B. Noris. | |
| Data stato definitivo: | 22-feb-2018 | |
| Appare nelle tipologie: | 4.01 Contributo in Atti di convegno |
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