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Successive iteration and positive solutions for a second-order multi-point boundary value problem on a half-line. (English) Zbl 1189.34057
Summary: This paper deals with the existence of positive solutions for some second-order multi-point boundary value problem on the half-line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.
MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B40Boundary value problems for ODE on infinite intervals
References:
[1]Chen, S.; Zhang, Y.: Singular boundary value problems on a half-line, J. math. Anal. appl. 195, 449-468 (1995) · Zbl 0852.34019 · doi:10.1006/jmaa.1995.1367
[2]Liu, X.: Solutions of impulsive boundary value problems on the half-line, J. math. Anal. appl. 222, 411-430 (1998) · Zbl 0912.34021 · doi:10.1006/jmaa.1997.5908
[3]O’regan, D.: Theory of singular boundary value problems, (1994) · Zbl 0807.34028
[4]Zima, M.: On positive solution of boundary value problems on the half-line, J. math. Anal. appl. 259, 127-136 (2001) · Zbl 1003.34024 · doi:10.1006/jmaa.2000.7399
[5]Liu, Y.: Existence and unboundedness of positive solutions for singular boundary value problems on half-line, Appl. math. Comput. 144, 543-556 (2003) · Zbl 1036.34027 · doi:10.1016/S0096-3003(02)00431-9
[6]Lian, H.; Pang, H.; Ge, W.: Triple positive solutions for boundary value problems on infinite intervals, Nonlinear anal. 67, 2199-2207 (2007) · Zbl 1128.34011 · doi:10.1016/j.na.2006.09.016
[7]Yan, B.: Boundary value problems on the half-line with impulses and infinite delay, J. math. Anal. appl. 259, 94-114 (2001) · Zbl 1009.34059 · doi:10.1006/jmaa.2000.7392
[8]Ma, D.; Du, Z.; Ge, W.: Existence and iteration of monotone positive solutions for multipoint boundary value problems with p-Laplacian operator, Comput. math. Appl. 50, 729-739 (2005) · Zbl 1095.34009 · doi:10.1016/j.camwa.2005.04.016
[9]Sun, B.; Ge, W.: Existence and iteration of positive solutions for some p-Laplacian boundary value problems, Nonlinear anal. 67, 1820-1830 (2007) · Zbl 1122.34307 · doi:10.1016/j.na.2006.08.025
[10]Sun, B.; Ge, W.: Successive iteration and positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problems, Appl. math. Comput. 188, 1772-1779 (2007) · Zbl 1119.65072 · doi:10.1016/j.amc.2006.11.040
[11]Il’in, V. A.; Moiseer, E. I.: Nonlocal boundary value problem of the first kind for a Sturm–Liouville operator in its differential and finite difference aspects, Differ. equ. 23, 803-810 (1987) · Zbl 0668.34025
[12]Gupta, C. P.: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations, J. math. Anal. appl. 168, 540-551 (1992) · Zbl 0763.34009 · doi:10.1016/0022-247X(92)90179-H
[13]Zhang, Z. X.; Wang, J. Y.: The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems, J. comput. Appl. math. 147, 41-52 (2002) · Zbl 1019.34021 · doi:10.1016/S0377-0427(02)00390-4
[14]Xu, X.: Positive solutions for singular m-point boundary value problems with positive parameter, J. math. Anal. appl. 291, 352-367 (2004) · Zbl 1047.34016 · doi:10.1016/j.jmaa.2003.11.009
[15]Sun, J. X.; Xu, X.; O’regan, D.: Nodal solutions for m-point boundary value problems using bifurcation methods, Nonlinear anal. 68, 3034-3046 (2008) · Zbl 1141.34009 · doi:10.1016/j.na.2007.02.043
[16]Zhang, X. G.; Liu, L. S.: Positive solutions of fourth-order multi-point boundary value problems with bending term, Appl. math. Comput. 194, 321-332 (2007) · Zbl 1193.34050 · doi:10.1016/j.amc.2007.04.028