Existence and Concentration Behavior of Positive Solutions For a Kirchhoff Equation in R3
Bressan, Alberto and Chow, Shui-Nee and Mallet-Paret, John and Ni, Wei-Ming
We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem where ε>0 is a parameter and a,b>0 are constants; V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term. We relate the number of solutions with the topology of the set where V attains its minimum. The results are proved by using the variational methods.
X. He and W. Zou, "Existence and Concentration Behavior of Positive Solutions For a Kirchhoff Equation in R3," Journal of Differential Equations, Elsevier, Jan 2012.
The definitive version is available at https://doi.org/10.1016/j.jde.2011.08.035
Mathematics and Statistics
Keywords and Phrases
Positive Solutions; Kirchoff Type Equation; Variational Methods
Article - Journal
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