Existence results for singular nonlinear BVPs in the critical regime
We study the existence of solutions for a class of boundary value problems on the half line, associated to a third order ordinary differential equation of the type $$\left(\Phi(k(t, u'(t))u''(t))\right)'(t)=f \left(t, u(t), u'(t), u''(t) \right), \quad\mbox {a.a....
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University of Szeged
2024-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10963 |
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| author | Francesca Anceschi Giuseppina Autuori Francesca Papalini |
| author_facet | Francesca Anceschi Giuseppina Autuori Francesca Papalini |
| author_sort | Francesca Anceschi |
| collection | DOAJ |
| description | We study the existence of solutions for a class of boundary value problems on the half line, associated to a third order ordinary differential equation of the type
$$\left(\Phi(k(t, u'(t))u''(t))\right)'(t)=f \left(t, u(t), u'(t), u''(t) \right), \quad\mbox {a.a. } t\in\mathbb{R}^+_0.$$
The prototype for the operator $\Phi$ is the $\Phi$-Laplacian; the function $k$ is assumed to be continuous and it may vanish in a subset of zero Lebesgue measure, so that the problem can be singular; finally, $f$ is a Carathéodory function satisfying a weak growth condition of Winter–Nagumo type. The approach we follow is based on fixed point techniques combined with the upper and lower solutions method. |
| format | Article |
| id | doaj-art-17d704b8cfc442c48dd3b004e5a734eb |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-17d704b8cfc442c48dd3b004e5a734eb2025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-07-0120243513410.14232/ejqtde.2024.1.3510963Existence results for singular nonlinear BVPs in the critical regimeFrancesca Anceschi0https://orcid.org/0000-0001-7594-3511Giuseppina AutuoriFrancesca Papalini1Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, ItalyDipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, ItalyWe study the existence of solutions for a class of boundary value problems on the half line, associated to a third order ordinary differential equation of the type $$\left(\Phi(k(t, u'(t))u''(t))\right)'(t)=f \left(t, u(t), u'(t), u''(t) \right), \quad\mbox {a.a. } t\in\mathbb{R}^+_0.$$ The prototype for the operator $\Phi$ is the $\Phi$-Laplacian; the function $k$ is assumed to be continuous and it may vanish in a subset of zero Lebesgue measure, so that the problem can be singular; finally, $f$ is a Carathéodory function satisfying a weak growth condition of Winter–Nagumo type. The approach we follow is based on fixed point techniques combined with the upper and lower solutions method.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10963boundary value problems on unbounded domainsheteroclinic solutions$\phi$-laplacian operatorsingular equationswintner–nagumo conditionthird order odes |
| spellingShingle | Francesca Anceschi Giuseppina Autuori Francesca Papalini Existence results for singular nonlinear BVPs in the critical regime Electronic Journal of Qualitative Theory of Differential Equations boundary value problems on unbounded domains heteroclinic solutions $\phi$-laplacian operator singular equations wintner–nagumo condition third order odes |
| title | Existence results for singular nonlinear BVPs in the critical regime |
| title_full | Existence results for singular nonlinear BVPs in the critical regime |
| title_fullStr | Existence results for singular nonlinear BVPs in the critical regime |
| title_full_unstemmed | Existence results for singular nonlinear BVPs in the critical regime |
| title_short | Existence results for singular nonlinear BVPs in the critical regime |
| title_sort | existence results for singular nonlinear bvps in the critical regime |
| topic | boundary value problems on unbounded domains heteroclinic solutions $\phi$-laplacian operator singular equations wintner–nagumo condition third order odes |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10963 |
| work_keys_str_mv | AT francescaanceschi existenceresultsforsingularnonlinearbvpsinthecriticalregime AT giuseppinaautuori existenceresultsforsingularnonlinearbvpsinthecriticalregime AT francescapapalini existenceresultsforsingularnonlinearbvpsinthecriticalregime |