Existence and nonexistence of positive radial solutions of a quasilinear Dirichlet problem with diffusion
| Autor: | Laura Baldelli, Valentina Brizi, Roberta Filippucci |
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| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Analysis of PDEs
35J92 (Primary) 35B45 35B53 35J60 (Secondary) Quasilinear elliptic equations A priori estimates Liouville theorems Existence and nonexistence results Positive radial solutions Quasilinear elliptic equations Liouville theorems Applied Mathematics FOS: Mathematics A priori estimates Existence and nonexistence results Positive radial solutions Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Differential Equations. 359:107-151 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2023.02.034 |
| Popis: | In this paper existence and nonexistence results of positive radial solutions of a Dirichlet $m$-Laplacian problem with different weights and a diffusion term inside the divergence of the form $\big(a(|x|)+g(u)\big)^{-\gamma}$, with $\gamma>0$ and $a$, $g$ positive functions satisfying natural growth conditions, are proved. Precisely, we obtain a new critical exponent $m^*_{\alpha,\beta,\gamma}$, which extends the one relative to case with no diffusion and it divides existence from nonexistence of positive radial solutions. The results are obtained via several tools such as a suitable modification of the celebrated blow up technique, Liouville type theorems, a fixed point theorem and a Poho\v zaev-Pucci-Serrin type identity. |
| Databáze: | OpenAIRE |
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