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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/143741 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |