Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions
In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-06-01
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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=4229 |
| Summary: | In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface $\mathcal{C}$ which separates $\mathbb{R}_+^2 \times (0,\infty)$ into two regions $\mathcal{O}_1$ and $\mathcal{O}_2$ such that the problem under consideration has two positive solutions for $( \mu,\lambda) \in \mathcal{O}_1,$ at least one positive solution for $( \mu,\lambda) \in \mathcal{C}$, and no positive solutions for $( \mu,\lambda) \in \mathcal{O}_2.$ |
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| ISSN: | 1417-3875 |