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Existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions. (English) Zbl 1235.34179
The author uses a fixed point theorem due to R. I. Avery and A. C. Peterson [Comput. Math. Appl. 42, 313–322 (2001; Zbl 1005.47051)] to establish the existence of at least three non-negative solutions of some nonlocal boundary value problems to third order differential equations with arbitrary continuous advanced arguments. An example is given to illustrate the main results.
MSC:
34K10Boundary value problems for functional-differential equations
47N20Applications of operator theory to differential and integral equations
References:
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[9]Webb, J. R. L.; Infante, G.: Positive solutions of nonlocal boundary value problems: a unified approach, J. lond. Math. soc. 74, 673-693 (2006) · Zbl 1115.34028 · doi:10.1112/S0024610706023179
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[11]Infante, G.; Pietramala, P.; Zima, M.: Positive solutions for a class of nonlocal impulsive BVPs via fixed point index, Topol. methods nonlinear anal. 36, 263-284 (2010)
[12]Jankowski, T.: Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions, Nonlinear anal. 74, 3775-3785 (2011) · Zbl 1221.34071 · doi:10.1016/j.na.2011.03.022
[13]Karakostos, G. L.; Tsamatos, P. Ch.: Existence of multipoint positive solutions for a nonlocal boundary value problem, Topol. methods nonlinear anal. 19, 109-121 (2002) · Zbl 1071.34023
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