Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions
We prove the existence of positive solutions for the \(p\)-Laplacian problem \[\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}\] where \(\phi (s)=|s|^{p-2}s\), \(p\gt 1\), \(H_{i}:\mathbb{R}...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3938.pdf |
| _version_ | 1819315446357164032 |
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| author | D. D. Hai X. Wang |
| author_facet | D. D. Hai X. Wang |
| author_sort | D. D. Hai |
| collection | DOAJ |
| description | We prove the existence of positive solutions for the \(p\)-Laplacian problem \[\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}\] where \(\phi (s)=|s|^{p-2}s\), \(p\gt 1\), \(H_{i}:\mathbb{R}\rightarrow\mathbb{R}\) can be nonlinear, \(i=1,2\), \(f:(0,\infty )\rightarrow \mathbb{R}\) is \(p\)-superlinear or \(p\)-sublinear at \(\infty\) and is allowed be singular \((\pm\infty)\) at \(0\), and \(\lambda\) is a positive parameter. |
| first_indexed | 2024-12-24T10:00:14Z |
| format | Article |
| id | doaj.art-563a8fef20564dd485850f1f614e9520 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-24T10:00:14Z |
| publishDate | 2019-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-563a8fef20564dd485850f1f614e95202022-12-21T17:01:07ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01395675689https://doi.org/10.7494/OpMath.2019.39.5.6753938Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditionsD. D. Hai0https://orcid.org/0000-0002-9927-0793X. Wang1https://orcid.org/0000-0001-5584-5009Mississippi State University, Department of Mathematics and Statistics, Mississippi State, MS 39762, USAMississippi State University, Department of Mathematics and Statistics, Mississippi State, MS 39762, USAWe prove the existence of positive solutions for the \(p\)-Laplacian problem \[\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}\] where \(\phi (s)=|s|^{p-2}s\), \(p\gt 1\), \(H_{i}:\mathbb{R}\rightarrow\mathbb{R}\) can be nonlinear, \(i=1,2\), \(f:(0,\infty )\rightarrow \mathbb{R}\) is \(p\)-superlinear or \(p\)-sublinear at \(\infty\) and is allowed be singular \((\pm\infty)\) at \(0\), and \(\lambda\) is a positive parameter.https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3938.pdf\(p\)-laplaciansemipositonenonlinear boundary conditionspositive solutions |
| spellingShingle | D. D. Hai X. Wang Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions Opuscula Mathematica \(p\)-laplacian semipositone nonlinear boundary conditions positive solutions |
| title | Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions |
| title_full | Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions |
| title_fullStr | Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions |
| title_full_unstemmed | Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions |
| title_short | Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions |
| title_sort | positive solutions for the one dimensional p laplacian with nonlinear boundary conditions |
| topic | \(p\)-laplacian semipositone nonlinear boundary conditions positive solutions |
| url | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3938.pdf |
| work_keys_str_mv | AT ddhai positivesolutionsfortheonedimensionalplaplacianwithnonlinearboundaryconditions AT xwang positivesolutionsfortheonedimensionalplaplacianwithnonlinearboundaryconditions |