On a class of singular Trudinger-Moser type inequalities and its applications
On a class of singular Trudinger-Moser type inequalities and its applications
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DOI：
10.1002/mana.201000083
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发表时间：
2011-10
影响因子：
1
通讯作者：
Ó. JoãoMarcosdo;M. Souza
中科院分区：
文献类型：
--
作者：
Ó. JoãoMarcosdo;M. Souza
本文讨论了一类带奇异权的Trudinger-Moser不等式在任意光滑域上的嵌入问题，特别是对.作为这一结果的应用，利用Ekeland变分原理和山路定理，我们建立了如下一类问题弱解存在性和多解性的充分条件其中a ∈ [0，2），V（x）是一个远离零有界的连续正位势，且在无穷远处可以是“大的”，非线性函数f（s）的行为类似于当|S| +∞是一个小扰动。© 2011 WILEY-VCH Verlag GmbH & Co. KGaA，魏因海姆
This paper deals with an improvement of a class of the Trudinger-Moser inequality with a singular weight associated to the embedding of the standard Sobolev space H10(Ω) into Orlicz spaces for any smooth domain , in particular for . As an application of this result, using the Ekeland variational principle and the mountain-pass theorem we establish sufficient conditions for the existence and multiplicity of weak solutions for the following class of problems where a ∈ [0, 2), V(x) is a continuous positive potential bounded away from zero and which can be “large” at the infinity, the nonlinearity f(s) behaves like when |s| +∞ and is a small perturbation. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim