Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity
We consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u, x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)uq-2u; however, the nonlinearity f(x,u)...
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| Format: | Article |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/7935706 |
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| author | Huxiao Luo Shengjun Li Wenfeng He |
| author_facet | Huxiao Luo Shengjun Li Wenfeng He |
| author_sort | Huxiao Luo |
| collection | DOAJ |
| description | We consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u, x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)uq-2u; however, the nonlinearity f(x,u)-Γ(x)uq-2u may change sign. If V is coercive, we investigate the existence of ground state solutions for p-Laplacian equation. |
| format | Article |
| id | doaj-art-7a858035ba2140eda70d398651a2b619 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7a858035ba2140eda70d398651a2b6192025-02-03T01:07:00ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/79357067935706Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing NonlinearityHuxiao Luo0Shengjun Li1Wenfeng He2Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaCollege of Information Sciences and Technology, Hainan University, Haikou 570228, ChinaCollege of Information Sciences and Technology, Hainan University, Haikou 570228, ChinaWe consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u, x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)uq-2u; however, the nonlinearity f(x,u)-Γ(x)uq-2u may change sign. If V is coercive, we investigate the existence of ground state solutions for p-Laplacian equation.http://dx.doi.org/10.1155/2018/7935706 |
| spellingShingle | Huxiao Luo Shengjun Li Wenfeng He Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity Journal of Function Spaces |
| title | Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity |
| title_full | Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity |
| title_fullStr | Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity |
| title_full_unstemmed | Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity |
| title_short | Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity |
| title_sort | non nehari manifold method for fractional p laplacian equation with a sign changing nonlinearity |
| url | http://dx.doi.org/10.1155/2018/7935706 |
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