| Автор | Shi, Beibei |
| Автор | Dong, Yujun |
| Автор | Huang, Qi |
| Дата выпуска | 2007 |
| dc.description | In this paper, we first investigate the classification of positively homogeneous equations $(\phi_p(u'))'+q(t)\phi_p(u)=0$, $u(0)=0=u(1)$, where $p>1$ is fixed, $\phi_p(u)=|u|^{p-2}u$ and $q\in L^{\infty}(0,1)$, and then discuss the existence of solutions for non-homogeneous equations. The main method of classification is by using a generalized Prufer equation $$ \theta'=|\4\cos_p\theta|^p+\frac{q(t)}{p-1}|\4\sin_p\theta|^p\quad\text{for }t\in(0,1), $$ where $\sin_p:\mathbb{R}\to[-1,1]$ is a periodic function and $\cos_pt=\mathrm{d}\sin_pt/\mathrm{d} t$ for $t\in\mathbb{R}$. |
| Издатель | Cambridge University Press |
| Название | An index classification theory of homogeneous p-Laplacian equations and existence of solutions of non-homogeneous equations |
| DOI | 10.1017/S0308210505000454 |
| Electronic ISSN | 1473-7124 |
| Print ISSN | 0308-2105 |
| Журнал | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| Том | 137 |
| Первая страница | 183 |
| Последняя страница | 194 |
| Аффилиация | Shi Beibei; Nanjing Normal University; Nanjing Xiaozhuang College |
| Аффилиация | Dong Yujun; Nanjing Normal University |
| Аффилиация | Huang Qi; Southern Yangtzr University |
| Выпуск | 1 |
