Semiclassical Solutions for a Kind of Coupled Schrödinger Equations
In this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2<p<2∗,2<q<2∗,2∗=2N/N−2, andN≥3; λ>0 is a parameter; and a1,a2,a3,b1,b2,b3,c∈CℝN,ℝ and u,v∈H1ℝN. Under some suitable co...
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/4378691 |
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| author | Jinmei Fan Yi-rong Jiang Qiongfen Zhang |
| author_facet | Jinmei Fan Yi-rong Jiang Qiongfen Zhang |
| author_sort | Jinmei Fan |
| collection | DOAJ |
| description | In this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2<p<2∗,2<q<2∗,2∗=2N/N−2, andN≥3; λ>0 is a parameter; and a1,a2,a3,b1,b2,b3,c∈CℝN,ℝ and u,v∈H1ℝN. Under some suitable conditions that a10=infa1=0 or b10=infb1=0 and cx2≤ϑa1xb1x with ϑ∈0,1, the above coupled Schrödinger system possesses nontrivial solutions if λ∈0,λ0, where λ0 is related to a1,a2,a3,b1,b2,b3, and N. |
| format | Article |
| id | doaj-art-1d5ff9a1c82b44c2a3ba93aa22987292 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-1d5ff9a1c82b44c2a3ba93aa229872922025-08-20T03:54:38ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/43786914378691Semiclassical Solutions for a Kind of Coupled Schrödinger EquationsJinmei Fan0Yi-rong Jiang1Qiongfen Zhang2College of Science, Guilin University of Technology, Guilin, Guangxi 541004, ChinaCollege of Science, Guilin University of Technology, Guilin, Guangxi 541004, ChinaCollege of Science, Guilin University of Technology, Guilin, Guangxi 541004, ChinaIn this paper, we are concerned with the following coupled Schrödinger equations −λ2Δu+a1xu=cxv+a2xup−2u+a3xu2∗−2u,x∈ℝN,−λ2Δv+b1xv=cxu+b2xvp−2v+b3xv2∗−2v,x∈ℝN, where 2<p<2∗,2<q<2∗,2∗=2N/N−2, andN≥3; λ>0 is a parameter; and a1,a2,a3,b1,b2,b3,c∈CℝN,ℝ and u,v∈H1ℝN. Under some suitable conditions that a10=infa1=0 or b10=infb1=0 and cx2≤ϑa1xb1x with ϑ∈0,1, the above coupled Schrödinger system possesses nontrivial solutions if λ∈0,λ0, where λ0 is related to a1,a2,a3,b1,b2,b3, and N.http://dx.doi.org/10.1155/2020/4378691 |
| spellingShingle | Jinmei Fan Yi-rong Jiang Qiongfen Zhang Semiclassical Solutions for a Kind of Coupled Schrödinger Equations Advances in Mathematical Physics |
| title | Semiclassical Solutions for a Kind of Coupled Schrödinger Equations |
| title_full | Semiclassical Solutions for a Kind of Coupled Schrödinger Equations |
| title_fullStr | Semiclassical Solutions for a Kind of Coupled Schrödinger Equations |
| title_full_unstemmed | Semiclassical Solutions for a Kind of Coupled Schrödinger Equations |
| title_short | Semiclassical Solutions for a Kind of Coupled Schrödinger Equations |
| title_sort | semiclassical solutions for a kind of coupled schrodinger equations |
| url | http://dx.doi.org/10.1155/2020/4378691 |
| work_keys_str_mv | AT jinmeifan semiclassicalsolutionsforakindofcoupledschrodingerequations AT yirongjiang semiclassicalsolutionsforakindofcoupledschrodingerequations AT qiongfenzhang semiclassicalsolutionsforakindofcoupledschrodingerequations |