Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity
In this study, we consider the following quasilinear Choquard equation with singularity −Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u>0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1....
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2021
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oai:doaj.org-article:881bae44ac984bafbb872dc63356aadd2021-12-05T14:10:52ZExistence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity2391-545510.1515/math-2021-0025https://doaj.org/article/881bae44ac984bafbb872dc63356aadd2021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0025https://doaj.org/toc/2391-5455In this study, we consider the following quasilinear Choquard equation with singularity −Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u>0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where Iα{I}_{\alpha } is a Riesz potential, 0<α<N0\lt \alpha \lt N, and N+αN<p<N+αN−2\displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2}, with λ>0\lambda \gt 0. Under suitable assumption on VV and KK, we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions as λ→0\lambda \to 0.Shao LiuyangWang YingminDe Gruyterarticlequasilinear schrödinger equationsingularitychoquard typevariational methods35b0935j20MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 259-267 (2021) |
| institution |
DOAJ |
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DOAJ |
| language |
EN |
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quasilinear schrödinger equation singularity choquard type variational methods 35b09 35j20 Mathematics QA1-939 |
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quasilinear schrödinger equation singularity choquard type variational methods 35b09 35j20 Mathematics QA1-939 Shao Liuyang Wang Yingmin Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| description |
In this study, we consider the following quasilinear Choquard equation with singularity −Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u>0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}& x\in {{\mathbb{R}}}^{N},\end{array}\right. where Iα{I}_{\alpha } is a Riesz potential, 0<α<N0\lt \alpha \lt N, and N+αN<p<N+αN−2\displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2}, with λ>0\lambda \gt 0. Under suitable assumption on VV and KK, we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions as λ→0\lambda \to 0. |
| format |
article |
| author |
Shao Liuyang Wang Yingmin |
| author_facet |
Shao Liuyang Wang Yingmin |
| author_sort |
Shao Liuyang |
| title |
Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| title_short |
Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| title_full |
Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| title_fullStr |
Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| title_full_unstemmed |
Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity |
| title_sort |
existence and asymptotical behavior of solutions for a quasilinear choquard equation with singularity |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/881bae44ac984bafbb872dc63356aadd |
| work_keys_str_mv |
AT shaoliuyang existenceandasymptoticalbehaviorofsolutionsforaquasilinearchoquardequationwithsingularity AT wangyingmin existenceandasymptoticalbehaviorofsolutionsforaquasilinearchoquardequationwithsingularity |
| _version_ |
1718371648786137088 |