On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN
We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s∈0, 1, where Vx≥0 has a potential well and f:ℝN×ℝ→ℝ is a lower order perturbation of the critical power u2*s-2u. By employing the variational...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/143741 |
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| author | Zifei Shen Fashun Gao |
| author_facet | Zifei Shen Fashun Gao |
| author_sort | Zifei Shen |
| collection | DOAJ |
| description | We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s∈0, 1, where Vx≥0 has a potential well and f:ℝN×ℝ→ℝ is a lower order perturbation of the critical power u2*s-2u. By employing the variational method, we prove the existence of nontrivial solutions for the equation. |
| format | Article |
| id | doaj-art-ff2e3df3e2a448f4825e2e7c56bcdf31 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ff2e3df3e2a448f4825e2e7c56bcdf312025-02-03T06:14:04ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/143741143741On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝNZifei Shen0Fashun Gao1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaWe study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s∈0, 1, where Vx≥0 has a potential well and f:ℝN×ℝ→ℝ is a lower order perturbation of the critical power u2*s-2u. By employing the variational method, we prove the existence of nontrivial solutions for the equation.http://dx.doi.org/10.1155/2014/143741 |
| spellingShingle | Zifei Shen Fashun Gao On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN Abstract and Applied Analysis |
| title | On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN |
| title_full | On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN |
| title_fullStr | On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN |
| title_full_unstemmed | On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN |
| title_short | On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN |
| title_sort | on the existence of solutions for the critical fractional laplacian equation in rn |
| url | http://dx.doi.org/10.1155/2014/143741 |
| work_keys_str_mv | AT zifeishen ontheexistenceofsolutionsforthecriticalfractionallaplacianequationinrn AT fashungao ontheexistenceofsolutionsforthecriticalfractionallaplacianequationinrn |