Abstract and Applied Analysis

The Existence of Multiple Solutions for Nonhomogeneous Kirchhoff Type Equations in 3

Qi Zhang and Xiaoli Zhu

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Abstract

We are concerned with the existence of multiple solutions to the nonhomogeneous Kirchhoff type equation - ( a + b 3 | u | 2 ) Δ u + u = | u | p - 1 u + h ( x )   in   3 , where a ,   b are positive constants, p ( 1,5 ) ,   0 h ( x ) = h ( | x | ) C 1 ( 3 ) L 2 ( 3 ) , we can find a constant m p > 0 such that for all p ( 1,5 ) the equation has at least two radial solutions provided | h | 2 < m p .

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 806865, 5 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512172

Digital Object Identifier
doi:10.1155/2013/806865

Mathematical Reviews number (MathSciNet)
MR3134160

Citation

Zhang, Qi; Zhu, Xiaoli. The Existence of Multiple Solutions for Nonhomogeneous Kirchhoff Type Equations in ${ℝ}^{3}$. Abstr. Appl. Anal. 2013 (2013), Article ID 806865, 5 pages. doi:10.1155/2013/806865. https://projecteuclid.org/euclid.aaa/1393512172


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