Ground state solutions for fractional p-Kirchhoff equation
نویسندگان
چکیده
We study the fractional p-Kirchhoff equation $$ \Big( a+b \int_{\mathbb{R}^N}{\int_{\mathbb{R}^N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\, dx\, dy\Big) (-\Delta)_p^s u-\mu|u|^{p-2}u=|u|^{q-2}u, \quad x\in\mathbb{R}^N, where \((-\Delta)_p^s\) is p-Laplacian operator, a and b are strictly positive real numbers, \(s \in (0,1)\), \(1 < p< N/s,\) \(p< q< p^*_s-2\) with \(p^*_s=\frac{Np}{N-ps}\). By using variational method, we prove existence uniqueness of global minimum or mountain pass type critical points on \(L^p\)-normalized manifold\(S(c):=\big\{u\in W^{s,p}(\mathbb{R}^N): \int_{\mathbb{R}^N} |u|^pdx=c^p\big\}\).
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ژورنال
عنوان ژورنال: Electronic Journal of Differential Equations
سال: 2022
ISSN: ['1072-6691']
DOI: https://doi.org/10.58997/ejde.2022.61