Uniqueness of boundary blow-up solutions on exterior domain of RN
- 作者：Wei Dong ; Changci Pang
- 关键词：The first eigenvalue ; Exterior domain ; Boundary blow-up solution
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2007
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：1 June 2007
- 卷：330
- 期：1
- 页码：654-664
- 文件大小：141 K
摘要
In this paper, we consider the existence and uniqueness of positive solutions of the degenerate logistic type elliptic equation
le="margin-left: 25 !important; width: 600px !important">
lign="center"> lign="center" width="95%">l2">
le="margin-left: 25 !important; width: 600px !important"> where l3">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml3&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=03e53cc6388a66a128699ff4b443038a" title="Click to view the MathML source">N2, l4">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml4&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=d81b7ed8fa412af11235e15abd1c47c4" title="Click to view the MathML source">DRN is a bounded domain with smooth boundary and l5">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml5&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=d32ffe06ff8aeca40709b1c5e5bc0f77" title="Click to view the MathML source">a(x), l6">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml6&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=60b7a043ba285d6f621d08b642d25eba" title="Click to view the MathML source">b(x) are continuous functions on l7">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml7&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=0d5ed65cd8b8e5bf0e116aa34e4d47d4" title="Click to view the MathML source">RN with l8">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml8&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=06520ad8cefdcc6984d3e0a41a311dff" title="Click to view the MathML source">b(x)0, l9">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml9&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=89020c7ce5032b0d9ed26209adacfb1f" title="Click to view the MathML source">b(x)0. We show that under rather general conditions on l10">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml10&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=c403090bfcec8af55c129c080038c35b" title="Click to view the MathML source">a(x) and l11">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml11&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=f366a5048517de227e65b8acb91135e5" title="Click to view the MathML source">b(x) for large l12">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml12&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=d0d68d91f3dfde06a362588b67eaea84" title="Click to view the MathML source">|x|, there exists a unique positive solution. Our results improve the corresponding ones in [W. Dong, Y. Du, Unbounded principal eigenfunctions and the logistic equation on l13">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml13&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=71082806e7540be06a70a4eebd8b245c" title="Click to view the MathML source">RN, Bull. Austral. Math. Soc. 67 (2003) 413–427] and [Y. Du, L. Ma, Logistic type equations on l14">le="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4KV2YJV-8&_mathId=mml14&_user=10&_cdi=6894&_rdoc=51&_acct=C000050221&_version=1&_userid=10&md5=ff90d8c0b291e264b1ec20c251466581" title="Click to view the MathML source">RN by a squeezing method involving boundary blow-up solutions, J. London Math. Soc. (2) 64 (2001) 107–124].