A Palais-Smale Approach to Lane-Emden Equations

• Main Authors: Huei-Li Lin, 林惠莉
• Other Authors: Hwai-Chiaun Wang
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/84705845795015514792

碩士 === 國立清華大學 === 數學系 === 87 === Chen-Lee-Wang [5], Chen-Wang [6], and Lien-Tzeng-Wang [14] asserted the existence of a ground state solution of equation (UD) in interior flask domains $\Bbb D_{s}^{r}$ : there exists $s_{0}>0$ such that the index $\alpha (\Bbb D_{s}^{r})$\ admits a ground state solution if $s>s_{0}$, but $\alpha (\ Bbb D_{s}^{r})$ does not admit any ground state solution if $s<s_{0}$. There is an open question: is $s_{0}=r$? In this article, we establish an index comparison criterion, then use the criterion to assert that there exists a ground state solution of equation (UD) in a flat interior flask domain : the Esteban-Lions domain $\Bbb {S}_{0}^{r}$ by adding an arbitrary small width but sufficient long corridor. We also establish the asymptotic behavior, the symmetry, and the algorithms and visualization of each solution of equation (UD) in the interior flask domain $\ Bbb D_{s}^{r}$.