Existence of solutions to a superlinear p-Laplacian equation
Using Morse theory, we establish the existence of solutions to the equation $-Delta_p u = f(x,u)$ with Dirichlet boundary conditions. We assume that $int_0^s f(x,t),dt$ lies between the first two eigenvalues of the p-Laplacian.
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| Format: | Article |
| Language: | English |
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Texas State University
2001-10-01
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| Series: | Electronic Journal of Differential Equations |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2001/66/abstr.html |
| _version_ | 1819134605391822848 |
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| author | Shibo Liu |
| author_facet | Shibo Liu |
| author_sort | Shibo Liu |
| collection | DOAJ |
| description | Using Morse theory, we establish the existence of solutions to the equation $-Delta_p u = f(x,u)$ with Dirichlet boundary conditions. We assume that $int_0^s f(x,t),dt$ lies between the first two eigenvalues of the p-Laplacian. |
| first_indexed | 2024-12-22T10:05:51Z |
| format | Article |
| id | doaj.art-0caa0d13bbdd4cb59d186bc76f61afb3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T10:05:51Z |
| publishDate | 2001-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0caa0d13bbdd4cb59d186bc76f61afb32022-12-21T18:29:57ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912001-10-0120016616Existence of solutions to a superlinear p-Laplacian equationShibo LiuUsing Morse theory, we establish the existence of solutions to the equation $-Delta_p u = f(x,u)$ with Dirichlet boundary conditions. We assume that $int_0^s f(x,t),dt$ lies between the first two eigenvalues of the p-Laplacian.http://ejde.math.txstate.edu/Volumes/2001/66/abstr.html |
| spellingShingle | Shibo Liu Existence of solutions to a superlinear p-Laplacian equation Electronic Journal of Differential Equations |
| title | Existence of solutions to a superlinear p-Laplacian equation |
| title_full | Existence of solutions to a superlinear p-Laplacian equation |
| title_fullStr | Existence of solutions to a superlinear p-Laplacian equation |
| title_full_unstemmed | Existence of solutions to a superlinear p-Laplacian equation |
| title_short | Existence of solutions to a superlinear p-Laplacian equation |
| title_sort | existence of solutions to a superlinear p laplacian equation |
| url | http://ejde.math.txstate.edu/Volumes/2001/66/abstr.html |
| work_keys_str_mv | AT shiboliu existenceofsolutionstoasuperlinearplaplacianequation |