A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains
碩士 === 國立清華大學 === 數學系 === 87 === Chen-Lee-Wang [CLW], Chen-Wang [CW], and Lien-Tzeng-Wang [LTW] 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...
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ndltd-TW-087NTHU04790212015-10-13T11:46:55Z http://ndltd.ncl.edu.tw/handle/54217823784878345220 A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains 在無界域上用巴萊斯麥爾法解半線性橢圓方程 Chiau-Ing Lin 林巧瑩 碩士 國立清華大學 數學系 87 Chen-Lee-Wang [CLW], Chen-Wang [CW], and Lien-Tzeng-Wang [LTW] 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 $s<s_0.$ Is the Esteban-Lions domain $\Bbb D_r^r$ sharp for the existence of solutions: $s_0=r$? In this article, we answer this question partially: there exists a ground state solution of equation (UDf) in a flat interior flask domain : the Esteban-Lions domain $\Bbb S_0^r$ by adding an arbitrary small width but sufficient long corridor. In order to assert our main result, we establish an index comparison criterion: if $\alpha (\Omega) <\alpha (\tilde \Omega_n)$ for some $n$, then there is a ground state solution of equation (UDf) in $\Omega$. We also establish the asymptotic behavior and the symmetry of each solution of equation (UDf) in the interior flask domain $\Bbb D_s^r$. Hwai-Chiaun Wang 王懷權 1999 學位論文 ; thesis 27 en_US |
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碩士 === 國立清華大學 === 數學系 === 87 === Chen-Lee-Wang [CLW], Chen-Wang [CW], and Lien-Tzeng-Wang [LTW] 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 $s<s_0.$ Is the Esteban-Lions
domain $\Bbb D_r^r$ sharp for the existence of solutions: $s_0=r$? In this article, we answer this
question partially: there exists a ground state solution of equation (UDf) in a flat interior flask domain :
the Esteban-Lions domain $\Bbb S_0^r$ by adding an arbitrary small width but sufficient long corridor.
In order to assert our main result, we establish an index comparison criterion: if $\alpha (\Omega) <\alpha
(\tilde \Omega_n)$ for some $n$, then there is a ground state solution of equation (UDf) in $\Omega$.
We also establish the asymptotic behavior and the symmetry of each solution of equation (UDf) in the
interior flask domain $\Bbb D_s^r$.
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Hwai-Chiaun Wang |
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Hwai-Chiaun Wang Chiau-Ing Lin 林巧瑩 |
author |
Chiau-Ing Lin 林巧瑩 |
spellingShingle |
Chiau-Ing Lin 林巧瑩 A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
author_sort |
Chiau-Ing Lin |
title |
A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
title_short |
A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
title_full |
A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
title_fullStr |
A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
title_full_unstemmed |
A Palais-Smale Approach to Semilinear Elliptic Equations in Unbounded Domains |
title_sort |
palais-smale approach to semilinear elliptic equations in unbounded domains |
publishDate |
1999 |
url |
http://ndltd.ncl.edu.tw/handle/54217823784878345220 |
work_keys_str_mv |
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