Abstract
The paper presents new existence, localization and multiplicity results for positive solutions of ordinary differential equations or systems of the form $(\phi(u'))' + f(t, u) = 0$, where $\phi : (-a, a) \to (-b, b)$, $0 \lt a, b \leq \infty$, is some homeomorphism such that $\phi(0) = 0$. Our approach is based on Krasnosel'skiĭ type compression-expansion arguments and on a weak Harnack type inequality for positive supersolutions of the operator $(\phi(u'))'$. In the case of the systems, the localization of solutions is obtained in a component-wise manner. The theory applies in particular to equations and systems with $p$-Laplacian, bounded or singular homeomorphisms.
Citation
Diana-Raluca Herlea. Radu Precup. "Existence, Localization and Multiplicity of Positive Solutions to $\phi$-Laplace Equations and Systems." Taiwanese J. Math. 20 (1) 77 - 89, 2016. https://doi.org/10.11650/tjm.20.2016.5553
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