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 $$\left(\Phi(k(t, u'(t))u''(t))\right)'(t)=f \left(t, u(t), u'(t), u''(t) \right), \quad\mbox {a.a....
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10963 |
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| Summary: | We study the existence of solutions for a class of boundary value problems on the half line, associated to a third order ordinary differential equation of the type
$$\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. |
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| ISSN: | 1417-3875 |