Antimaximum principle for quasilinear problems
| Autor: | Arcoya, D., Julio D Rossi |
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| Rok vydání: | 2004 |
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| Zdroj: | Adv. Differential Equations 9, no. 9-10 (2004), 1185-1200 Scopus-Elsevier |
| ISSN: | 1079-9389 |
| DOI: | 10.57262/ade/1355867918 |
| Popis: | In this paper, for a bounded, smooth domain $\Omega \subset {{\mathbb {R}}}^N$, $h\in L^r(\Omega)$, $r>N/2$, $g\in L^s(\partial \Omega)$, $s>N-1$, we prove the maximum and antimaximum principle for the quasilinear boundary-value problem $- \mbox{div} ( A(u) \nabla u) +u = h$ in $\Omega$, $ A(u) \nabla u \cdot \eta = \lambda f(u) + g$, on $\partial \Omega$, where $A$ is elliptic and bounded and $f$ is asymptotically linear. The sharpness of this result ($r>N/2$ and $s>N-1$) is discussed for the linear boundary-value problem, $-\Delta u + u = h$ in $\Omega$, $\partial u/\partial\eta = \lambda u + g $ on $\partial \Omega$. |
| Databáze: | OpenAIRE |
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