Abstract and Applied Analysis

Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R 3

Ling Ding, Lin Li, and Jin-Ling Zhang

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Abstract

We study the following nonhomogeneous Kirchhoff equation: - ( a + b R 3 | u | 2 d x ) Δ u + u = k ( x ) f ( u ) + h ( x ) ,   x R 3 ,   u H 1 ( R 3 ) ,   u > 0 ,   x R 3 , where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k , f , and h , existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 710949, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273194

Digital Object Identifier
doi:10.1155/2014/710949

Mathematical Reviews number (MathSciNet)
MR3176766

Zentralblatt MATH identifier
07022928

Citation

Ding, Ling; Li, Lin; Zhang, Jin-Ling. Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in ${R}^{3}$. Abstr. Appl. Anal. 2014 (2014), Article ID 710949, 10 pages. doi:10.1155/2014/710949. https://projecteuclid.org/euclid.aaa/1412273194


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