Degenerate elliptic boundary value problems with asymptotically linear nonlinearity
Degenerate elliptic boundary value problems with asymptotically linear nonlinearity
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DOI：
10.1007/s12215-011-0052-4
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发表时间：
2011-07
影响因子：
1
通讯作者：
Kazuaki Taira
中科院分区：
文献类型：
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作者：
Kazuaki Taira
研究了一类具有渐近线性非线性的半线性退化椭圆型边值问题，其中包括Dirichlet和Robin问题。我们的方法是基于巴拿赫空间之间的全局反转定理，并以广泛使用偏微分方程理论中最新发展的思想和技术为特点。利用变分方法，证明了问题的存在唯一性定理。本文的结果将Ambrosetti和Prodi的三个定理推广到简并情形。
The purpose of this paper is to study a class of semilineardegenerateelliptic boundary value problems withasymptotically linear nonlinearitywhich include as particular cases the Dirichlet and Robin problems. Our approach is based on the global inversion theorems between Banach spaces, and is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. By making use of the variational method, we prove existence and uniqueness theorems for our problem. The results here extend three earlier theorems due to Ambrosetti and Prodi to the degenerate case.