Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth
We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}^{2}{\rm{d}}x\right){\left(-\Delta )}^{s}u+V\...
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De Gruyter
2025-04-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0075 |
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| author | Yang Jie Chen Haibo |
| author_facet | Yang Jie Chen Haibo |
| author_sort | Yang Jie |
| collection | DOAJ |
| description | We study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}^{2}{\rm{d}}x\right){\left(-\Delta )}^{s}u+V\left(x)u=\left({I}_{\mu }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N},\hspace{1.0em}\\ u\in {H}^{s}\left({{\mathbb{R}}}^{N}),\hspace{1.0em}\end{array}\right. where a,ba,b are positive constants, N>2sN\gt 2s, μ∈((N−4s)+,N)\mu \in \left({\left(N-4s)}_{+},N), s∈(0,1)s\in \left(0,1), and Iμ{I}_{\mu } is the Riesz potential. Considering the case that nonlinearity ff has critical growth, combining a monotonicity trick and global compactness lemma, we prove that the equation has a ground-state solution. Moreover, we study the regularity of ground-state solutions to the above equation, which extends the results in Moroz-Van Schaftingen [Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), 6557–6579] to the fractional Laplacian case. |
| format | Article |
| id | doaj-art-3960fda21cf846d3b054a3f3bb565458 |
| institution | DOAJ |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
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| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-3960fda21cf846d3b054a3f3bb5654582025-08-20T03:10:09ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-04-0114128147610.1515/anona-2025-0075Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growthYang Jie0Chen Haibo1School of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan 418008, PR ChinaSchool of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, PR ChinaWe study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}^{2}{\rm{d}}x\right){\left(-\Delta )}^{s}u+V\left(x)u=\left({I}_{\mu }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N},\hspace{1.0em}\\ u\in {H}^{s}\left({{\mathbb{R}}}^{N}),\hspace{1.0em}\end{array}\right. where a,ba,b are positive constants, N>2sN\gt 2s, μ∈((N−4s)+,N)\mu \in \left({\left(N-4s)}_{+},N), s∈(0,1)s\in \left(0,1), and Iμ{I}_{\mu } is the Riesz potential. Considering the case that nonlinearity ff has critical growth, combining a monotonicity trick and global compactness lemma, we prove that the equation has a ground-state solution. Moreover, we study the regularity of ground-state solutions to the above equation, which extends the results in Moroz-Van Schaftingen [Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), 6557–6579] to the fractional Laplacian case.https://doi.org/10.1515/anona-2025-0075kirchhoff-choquard equationfractionalground-state solutionpohozaev identity35r1149j35 |
| spellingShingle | Yang Jie Chen Haibo Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth Advances in Nonlinear Analysis kirchhoff-choquard equation fractional ground-state solution pohozaev identity 35r11 49j35 |
| title | Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth |
| title_full | Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth |
| title_fullStr | Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth |
| title_full_unstemmed | Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth |
| title_short | Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth |
| title_sort | ground state solutions for fractional kirchhoff choquard equations with critical growth |
| topic | kirchhoff-choquard equation fractional ground-state solution pohozaev identity 35r11 49j35 |
| url | https://doi.org/10.1515/anona-2025-0075 |
| work_keys_str_mv | AT yangjie groundstatesolutionsforfractionalkirchhoffchoquardequationswithcriticalgrowth AT chenhaibo groundstatesolutionsforfractionalkirchhoffchoquardequationswithcriticalgrowth |