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Yang, Dianwu

A variational principle for three-point boundary value problems with impulse. (English) Zbl 1474.34209

Abstr. Appl. Anal. 2014, Article ID 840408, 6 p. (2014).
Summary: We construct a variational functional of a class of three-point boundary value problems with impulse. Using the critical points theory, we study the existence of solutions to second-order three-point boundary value problems with impulse.

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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\textit{D. Yang}, Abstr. Appl. Anal. 2014, Article ID 840408, 6 p. (2014; Zbl 1474.34209)
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References:

[1] Bao, G.; Xu, X.; Song, Y., Positive solutions for three-point boundary value problems with a non-well-ordered upper and lower solution condition, Applied Mathematics Letters, 25, 4, 767-770, (2012) · Zbl 1248.34022
[2] Zhao, J.; Ge, W., A necessary and sufficient condition for the existence of positive solutions to a kind of singular three-point boundary value problem, Nonlinear Analysis: Theory, Methods and Applications, 71, 9, 3973-3980, (2009) · Zbl 1173.34316
[3] Li, F.; Jia, M.; Liu, X.; Li, C.; Li, G., Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order, Nonlinear Analysis: Theory, Methods and Applications, 68, 8, 2381-2388, (2008) · Zbl 1354.34043
[4] Li, F.; Sun, J.; Jia, M., Monotone iterative method for the second-order three-point boundary value problem with upper and lower solutions in the reversed order, Applied Mathematics and Computation, 217, 9, 4840-4847, (2011) · Zbl 1208.65107
[5] Pei, M.; Chang, S. K., The generalized quasilinearization method for second-order three-point boundary value problems, Nonlinear Analysis: Theory, Methods and Applications, 68, 9, 2779-2790, (2008) · Zbl 1336.34032
[6] Kwong, M. K.; Wong, J. S. W., Solvability of second-order nonlinear three-point boundary value problems, Nonlinear Analysis: Theory, Methods and Applications, 73, 8, 2343-2352, (2010) · Zbl 1202.34044
[7] Han, X., Positive solutions for a three-point boundary value problem at resonance, Journal of Mathematical Analysis and Applications, 336, 1, 556-568, (2007) · Zbl 1125.34014
[8] Liu, B.; Liu, L.; Wu, Y., Positive solutions for a singular second-order three-point boundary value problem, Applied Mathematics and Computation, 196, 2, 532-541, (2008) · Zbl 1138.34015
[9] Li, J.; Shen, J., Positive solutions for three-point boundary value problems for second-order impulsive differential equations on infinite intervals, Journal of Computational and Applied Mathematics, 235, 8, 2372-2379, (2011) · Zbl 1211.34034
[10] Liang, S.; Zhang, J., The existence of countably many positive solutions for some nonlinear singular three-point impulsive boundary value problems, Nonlinear Analysis: Theory, Methods and Applications, 71, 10, 4588-4597, (2009) · Zbl 1179.34026
[11] Jankowski, T., Positive solutions of three-point boundary value problems for second order impulsive differential equations with advanced arguments, Applied Mathematics and Computation, 197, 1, 179-189, (2008) · Zbl 1145.34355
[12] Sun, H.; Li, Y.; Nieto, J. J.; Tang, Q., Existence of solutions for Sturm-Liouville boundary value problem of impulsive differential equations, Abstract and Applied Analysis, 2012, (2012) · Zbl 1245.34030
[13] Nieto, J. J.; O’Regan, D., Variational approach to impulsive differential equations, Nonlinear Analysis: Real World Applications, 10, 680-690, (2009) · Zbl 1167.34318
[14] Tian, Y.; Ge, W., Variational methods to Sturm-Liouville boundary value problem for impulsive differential equations, Nonlinear Analysis: Theory, Methods and Applications, 72, 1, 277-287, (2010) · Zbl 1191.34038
[15] Tian, Y.; Ge, W., Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods, Journal of Mathematical Analysis and Applications, 387, 2, 475-489, (2012) · Zbl 1241.34032
[16] Zhang, H.; Li, Z., Variational approach to impulsive differential equations with periodic boundary conditions, Nonlinear Analysis: Real World Applications, 11, 1, 67-78, (2010) · Zbl 1186.34089
[17] Mawhin, J.; Willem, M., Critical Point Theory and Hamiltonian Systems, (1989), New York, NY, USA: Springer, New York, NY, USA · Zbl 0676.58017
[18] Bonanno, G.; Riccobono, G., Multiplicity results for Sturm-Liouville boundary value problems, Applied Mathematics and Computation, 210, 2, 294-297, (2009) · Zbl 1175.34028
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