Dirichlet problems for the p-Laplacian with a convection term
| Autor: | José C. Sabina de Lis, Jorge García-Melián, Peter Takáč |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
General Mathematics Weak solution Image (category theory) 010102 general mathematics Boundary (topology) 01 natural sciences Omega Dirichlet distribution 010101 applied mathematics symbols.namesake Domain (ring theory) symbols p-Laplacian Nabla symbol 0101 mathematics Mathematics |
| Zdroj: | Revista Matemática Complutense. 30:313-334 |
| ISSN: | 1988-2807 1139-1138 |
| DOI: | 10.1007/s13163-017-0227-4 |
| Popis: | We consider the nonlinear Dirichlet boundary value problem Open image in new window in a bounded domain \(\Omega \subset \mathbb {R}^N\) with smooth boundary \(\partial \Omega \), where \(\Delta _p u\mathop {=}\limits ^{\mathrm{{def}}}\mathrm {div} (|\nabla u|^{p-2} \nabla u)\) with \(1 0\)). When \(h\not \equiv 0\) and \(-\infty< \lambda < \lambda _1\), we prove that there exists a weak solution \(u\in W_0^{1,p}(\Omega )\) to problem (P); this solution is unique provided \(\lambda < 0\) (without any further assumptions). When \(h\ge 0\), \(h\not \equiv 0\), and \(0\le \lambda < \lambda _1\), we show that the solution is positive and also unique. |
| Databáze: | OpenAIRE |
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