Abstract and Applied Analysis

Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

Abstract

We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at $+\infty$ and $-\infty$ in ${\Bbb R}^{N}(N=2,3)$. Namely, it is 4-linear at $-\infty$ and 4-superlinear at $+\infty$. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 163645, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412276918

Digital Object Identifier
doi:10.1155/2014/163645

Mathematical Reviews number (MathSciNet)
MR3198153

Zentralblatt MATH identifier
07021842

Citation

Pei, Ruichang; Zhang, Jihui. Nontrivial Solutions for Asymmetric Kirchhoff Type Problems. Abstr. Appl. Anal. 2014 (2014), Article ID 163645, 8 pages. doi:10.1155/2014/163645. https://projecteuclid.org/euclid.aaa/1412276918

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