Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian
We study the existence of weak solutions to the following Neumann problem involving the p(x)-Laplacian operator: -Δp(x)u+e(x)|u|p(x)-2u=λa(x)f(u), in Ω, ∂u/∂ν=0, on ∂Ω. Under some appropriate conditions on the functions p, e, a, and f, we prove that there exists λ¯>0 such that any λ∈(0,λ¯)...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/632745 |
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| _version_ | 1849412166394839040 |
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| author | Qing Miao |
| author_facet | Qing Miao |
| author_sort | Qing Miao |
| collection | DOAJ |
| description | We study the existence of weak solutions to the following Neumann problem involving the p(x)-Laplacian operator: -Δp(x)u+e(x)|u|p(x)-2u=λa(x)f(u), in Ω, ∂u/∂ν=0, on ∂Ω. Under some appropriate conditions on the functions p, e, a, and f, we prove that there exists λ¯>0 such that any λ∈(0,λ¯) is an eigenvalue of the above problem. Our analysis mainly relies on variational arguments based on Ekeland’s variational principle. |
| format | Article |
| id | doaj-art-5a03c63d141c46a290ad9f5d244187dc |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-5a03c63d141c46a290ad9f5d244187dc2025-08-20T03:34:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/632745632745Eigenvalues for a Neumann Boundary Problem Involving the p(x)-LaplacianQing Miao0School of Mathematics and Computer Science, Yunnan Minzu University, Yunnan, Kunming 650500, ChinaWe study the existence of weak solutions to the following Neumann problem involving the p(x)-Laplacian operator: -Δp(x)u+e(x)|u|p(x)-2u=λa(x)f(u), in Ω, ∂u/∂ν=0, on ∂Ω. Under some appropriate conditions on the functions p, e, a, and f, we prove that there exists λ¯>0 such that any λ∈(0,λ¯) is an eigenvalue of the above problem. Our analysis mainly relies on variational arguments based on Ekeland’s variational principle.http://dx.doi.org/10.1155/2015/632745 |
| spellingShingle | Qing Miao Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian Advances in Mathematical Physics |
| title | Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian |
| title_full | Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian |
| title_fullStr | Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian |
| title_full_unstemmed | Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian |
| title_short | Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian |
| title_sort | eigenvalues for a neumann boundary problem involving the p x laplacian |
| url | http://dx.doi.org/10.1155/2015/632745 |
| work_keys_str_mv | AT qingmiao eigenvaluesforaneumannboundaryprobleminvolvingthepxlaplacian |