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2007 On nonnegative solutions of singular boundary-value problems for Emden-Fowler-type differential systems
Mariella Cecchi, Zuzana Došlá, Ivan Kiguradze, Mauro Marini
Differential Integral Equations 20(10): 1081-1106 (2007).

Abstract

We investigate some boundary-value problems for an Emden--Fowler-type differential system \[ u_{1}^{\prime}=g_{1}(t)u_{2}^{\lambda_{1}},\;\;\;u_{2}^{\prime}=g_{2} (t)u_{1}^{\lambda_{2}} \] on a finite or infinite interval $I=[a,b)$, where $g_{i}:I\rightarrow \lbrack0,\infty)$ $(i=1,2)$ are locally integrable functions. We give the optimal, in a certain sense, sufficient conditions that guarantee the existence of a unique (at least of one) nonnegative solution, satisfying one of the two following boundary conditions: \[ \mathrm{i)}\ u_{1}(a)=c_{0},\;\;\;\lim_{t\rightarrow b}u_{1}(t)=c;\;\; \mathrm{ii)}\ u_{2}(a)=c_{0},\;\;\;\lim_{t\rightarrow b}u_{1}(t)=c, \] in case $0\leq c_{0} < c < +\infty$ (in case $c_{0}\geq0$, $c=+\infty$ and $\lambda_{1}\lambda_{2}>1$). Moreover, the global two-sided estimations of the above-mentioned solutions are obtained together with applications to differential equations with $p$-Laplacian.

Citation

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Mariella Cecchi. Zuzana Došlá. Ivan Kiguradze. Mauro Marini. "On nonnegative solutions of singular boundary-value problems for Emden-Fowler-type differential systems." Differential Integral Equations 20 (10) 1081 - 1106, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.34044
MathSciNet: MR2365203

Subjects:
Primary: 34B16, 34B18, 34B40, 34C11

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 10 • 2007
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