Existence and concentration of ground-states for fractional Choquard equation with indefinite potential
This paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (−Δ)su+V(x)u=∫RNA(εy)∣u(y)∣p∣x−y∣μdyA(εx)∣u(x)∣p−2u(x),x∈RN,{\left(-\Delta )}^{s}u+V\left(x)u=\left(\mathop{\int }\limits_{{{\mathbb{...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-06-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0255 |
| _version_ | 1811185952347914240 |
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| author | Zhang Wen Yuan Shuai Wen Lixi |
| author_facet | Zhang Wen Yuan Shuai Wen Lixi |
| author_sort | Zhang Wen |
| collection | DOAJ |
| description | This paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (−Δ)su+V(x)u=∫RNA(εy)∣u(y)∣p∣x−y∣μdyA(εx)∣u(x)∣p−2u(x),x∈RN,{\left(-\Delta )}^{s}u+V\left(x)u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}\frac{A\left(\varepsilon y)| u(y){| }^{p}}{| x-y{| }^{\mu }}{\rm{d}}y\right)A\left(\varepsilon x)| u\left(x){| }^{p-2}u\left(x),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where s∈(0,1)s\in \left(0,1), N>2sN\gt 2s, 0<μ<2s0\lt \mu \lt 2s, 2<p<2N−2μN−2s2\lt p\lt \frac{2N-2\mu }{N-2s}, and ε\varepsilon is a positive parameter. Under some natural hypotheses on the potentials VV and AA, using the generalized Nehari manifold method, we obtain the existence of ground-state solutions. Moreover, we investigate the concentration behavior of ground-state solutions that concentrate at global maximum points of AA as ε→0\varepsilon \to 0. |
| first_indexed | 2024-04-11T13:38:04Z |
| format | Article |
| id | doaj.art-dff875e24f1e43d590f8e8e4da0dd845 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-11T13:38:04Z |
| publishDate | 2022-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-dff875e24f1e43d590f8e8e4da0dd8452022-12-22T04:21:24ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2022-06-011111552157810.1515/anona-2022-0255Existence and concentration of ground-states for fractional Choquard equation with indefinite potentialZhang Wen0Yuan Shuai1Wen Lixi2College of Science, Hunan University of Technology and Business, 410205 Changsha, Hunan, ChinaDepartment of Mathematics, University of Craiova, 200585 Craiova, Romania, China-Romania Research Center in Applied MathematicsDepartment of Mathematics, University of Craiova, 200585 Craiova, Romania, China-Romania Research Center in Applied MathematicsThis paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (−Δ)su+V(x)u=∫RNA(εy)∣u(y)∣p∣x−y∣μdyA(εx)∣u(x)∣p−2u(x),x∈RN,{\left(-\Delta )}^{s}u+V\left(x)u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}\frac{A\left(\varepsilon y)| u(y){| }^{p}}{| x-y{| }^{\mu }}{\rm{d}}y\right)A\left(\varepsilon x)| u\left(x){| }^{p-2}u\left(x),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where s∈(0,1)s\in \left(0,1), N>2sN\gt 2s, 0<μ<2s0\lt \mu \lt 2s, 2<p<2N−2μN−2s2\lt p\lt \frac{2N-2\mu }{N-2s}, and ε\varepsilon is a positive parameter. Under some natural hypotheses on the potentials VV and AA, using the generalized Nehari manifold method, we obtain the existence of ground-state solutions. Moreover, we investigate the concentration behavior of ground-state solutions that concentrate at global maximum points of AA as ε→0\varepsilon \to 0.https://doi.org/10.1515/anona-2022-0255fractional choquard equationconcentrationground-state solutions35a1535b0935j9258e05 |
| spellingShingle | Zhang Wen Yuan Shuai Wen Lixi Existence and concentration of ground-states for fractional Choquard equation with indefinite potential Advances in Nonlinear Analysis fractional choquard equation concentration ground-state solutions 35a15 35b09 35j92 58e05 |
| title | Existence and concentration of ground-states for fractional Choquard equation with indefinite potential |
| title_full | Existence and concentration of ground-states for fractional Choquard equation with indefinite potential |
| title_fullStr | Existence and concentration of ground-states for fractional Choquard equation with indefinite potential |
| title_full_unstemmed | Existence and concentration of ground-states for fractional Choquard equation with indefinite potential |
| title_short | Existence and concentration of ground-states for fractional Choquard equation with indefinite potential |
| title_sort | existence and concentration of ground states for fractional choquard equation with indefinite potential |
| topic | fractional choquard equation concentration ground-state solutions 35a15 35b09 35j92 58e05 |
| url | https://doi.org/10.1515/anona-2022-0255 |
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