Abstract and Applied Analysis

Multiple Solutions for a Class of N -Laplacian Equations with Critical Growth and Indefinite Weight

Guoqing Zhang and Ziyan Yao

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Abstract

Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N -Laplacian equations with critical growth and indefinite weight - div u N - 2 u + V x u N - 2 u = λ u N - 2 u / x β + f x , u / x β + ɛ h x , x N , u 0 , x N , where 0 < β < N , V ( x ) is an indefinite weight, f : N × behaves like exp α u N / N - 1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h ( W 1 , N ( N ) ) * .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 942092, 14 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395858341

Digital Object Identifier
doi:10.1155/2014/942092

Mathematical Reviews number (MathSciNet)
MR3166669

Citation

Zhang, Guoqing; Yao, Ziyan. Multiple Solutions for a Class of $N$ -Laplacian Equations with Critical Growth and Indefinite Weight. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 942092, 14 pages. doi:10.1155/2014/942092. https://projecteuclid.org/euclid.aaa/1395858341


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