Exact number of solutions for a Neumann problem involving the p-Laplacian
We study the exact number of solutions of the quasilinear Neumann boundary-value problem $$\displaylines{ (\varphi_p(u'(t)))'+g(u(t))=h(t)\quad\text{in } (a,b),\cr u'(a)=u'(b)=0, }$$ where $\varphi_p(s)=|s|^{p-2}s$ denotes the one-dimensional p-Laplacian. Under appropriat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/30/abstr.html |
| _version_ | 1828223706169606144 |
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| author | Justino Sanchez Vicente Vergara |
| author_facet | Justino Sanchez Vicente Vergara |
| author_sort | Justino Sanchez |
| collection | DOAJ |
| description | We study the exact number of solutions of the quasilinear Neumann
boundary-value problem
$$\displaylines{
(\varphi_p(u'(t)))'+g(u(t))=h(t)\quad\text{in } (a,b),\cr
u'(a)=u'(b)=0,
}$$
where $\varphi_p(s)=|s|^{p-2}s$ denotes the one-dimensional
p-Laplacian. Under appropriate hypotheses on g and h,
we obtain existence, multiplicity, exactness and
non existence results. The existence of solutions is
proved using the method of upper and lower solutions. |
| first_indexed | 2024-04-12T17:11:15Z |
| format | Article |
| id | doaj.art-637768df84594e4b852277ac99f68d95 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T17:11:15Z |
| publishDate | 2014-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-637768df84594e4b852277ac99f68d952022-12-22T03:23:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-01-01201430,110Exact number of solutions for a Neumann problem involving the p-LaplacianJustino Sanchez0Vicente Vergara1 Univ. de La Serena, Chile Univ. de Tarapaca, Arica, Chile We study the exact number of solutions of the quasilinear Neumann boundary-value problem $$\displaylines{ (\varphi_p(u'(t)))'+g(u(t))=h(t)\quad\text{in } (a,b),\cr u'(a)=u'(b)=0, }$$ where $\varphi_p(s)=|s|^{p-2}s$ denotes the one-dimensional p-Laplacian. Under appropriate hypotheses on g and h, we obtain existence, multiplicity, exactness and non existence results. The existence of solutions is proved using the method of upper and lower solutions.http://ejde.math.txstate.edu/Volumes/2014/30/abstr.htmlNeumann boundary value problemp-Laplacianlower-upper solutionsexact multiplicity |
| spellingShingle | Justino Sanchez Vicente Vergara Exact number of solutions for a Neumann problem involving the p-Laplacian Electronic Journal of Differential Equations Neumann boundary value problem p-Laplacian lower-upper solutions exact multiplicity |
| title | Exact number of solutions for a Neumann problem involving the p-Laplacian |
| title_full | Exact number of solutions for a Neumann problem involving the p-Laplacian |
| title_fullStr | Exact number of solutions for a Neumann problem involving the p-Laplacian |
| title_full_unstemmed | Exact number of solutions for a Neumann problem involving the p-Laplacian |
| title_short | Exact number of solutions for a Neumann problem involving the p-Laplacian |
| title_sort | exact number of solutions for a neumann problem involving the p laplacian |
| topic | Neumann boundary value problem p-Laplacian lower-upper solutions exact multiplicity |
| url | http://ejde.math.txstate.edu/Volumes/2014/30/abstr.html |
| work_keys_str_mv | AT justinosanchez exactnumberofsolutionsforaneumannprobleminvolvingtheplaplacian AT vicentevergara exactnumberofsolutionsforaneumannprobleminvolvingtheplaplacian |