Abstract
In this paper, we investigate the fractional p-Kirchhoff-type equation
where \({\lambda}\) is a real parameter, \({(-\Delta)_p^s }\) is the fractional p-Laplacian operator with \({0 < s < 1 < p}\) and \({ps < N}\), \({V(x), a(x), b(x): \mathbb{R}^N\to (0,\infty)}\) are three positive weights, and M is a continuous and positive function. The case \({1 < q < m < p_s^*}\) is considered. Using variational methods, we prove the existence, nonexistence, and multiplicity of solutions for the above equation depending on \({\lambda, m,q}\) and according to the weight functions a(x) and b(x). Our results extend the previous works of Pucci et al. [23] and of Xiang et al. [29].
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This work was supported by the Fundamental Research Funds for the Central Universities of China (2015B31014).
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Chen, C., Wei, Y. Existence, Nonexistence, and Multiple Results for the Fractional p-Kirchhoff-type Equation in \({\mathbb{R}^N}\) . Mediterr. J. Math. 13, 5077–5091 (2016). https://doi.org/10.1007/s00009-016-0793-6
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DOI: https://doi.org/10.1007/s00009-016-0793-6