Existence of a Positive Solution to Kirchhoff Problems Involving the Fractional Laplacian
Bin Ge
Harbin Engineering University, ChinaChao Zhang
Harbin Institute of Technology, China
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Abstract
The goal of this paper is to establish the existence of a positive solution to the following fractional Kirchhoff-type problem
where , is a parameter, , stands for the fractional Laplacian, . Using a variational method combined with suitable truncation techniques, we obtain the existence of at least one positive solution without compactness conditions.
Cite this article
Bin Ge, Chao Zhang, Existence of a Positive Solution to Kirchhoff Problems Involving the Fractional Laplacian. Z. Anal. Anwend. 34 (2015), no. 4, pp. 419–434
DOI 10.4171/ZAA/1547