Quasilinearization method and nonlocal singular three point boundary value problems
The method of upper and lower solutions and quasilinearization for nonlinear singular equations of the type $$-x''(t) +\lambda x'(t)= f(t,x(t)),\,t\in (0,1),$$ subject to nonlocal three-point boundary conditions $$x(0)=\delta x(\eta),\quad x(1)=0, \quad 0<\eta < 1,$$ are develop...
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| Published in | Electronic journal of qualitative theory of differential equations Vol. 2009; no. 17; pp. 1 - 13 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
University of Szeged
01.01.2009
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| Online Access | Get full text |
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| Summary: | The method of upper and lower solutions and quasilinearization for nonlinear singular equations of the type $$-x''(t) +\lambda x'(t)= f(t,x(t)),\,t\in (0,1),$$ subject to nonlocal three-point boundary conditions $$x(0)=\delta x(\eta),\quad x(1)=0, \quad 0<\eta < 1,$$ are developed. Existence of a $C^{1}$ positive solution is established. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solution of the nonlinear problem is obtained. |
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| ISSN: | 1417-3875 1417-3875 |
| DOI: | 10.14232/ejqtde.2009.4.17 |