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Keywords:
$p$-Laplacian operator; boundary value problem; impulsive differential equations; fixed-point theorem; positive solutions
$p$-Laplacian operator; boundary value problem; impulsive differential equations; fixed-point theorem; positive solutions
Summary:
In this paper, using a fixed point theorem on a convex cone, we consider the existence of positive solutions to the multipoint one-dimensional $p$-Laplacian boundary value problem with impulsive effects, and obtain multiplicity results for positive solutions.
References:
[1] Bai, Z., Ge, W.: Existence of three positive solutions for some second-order boundary value problems. Comput. Math. Appl. 48 (2004), 699-707. DOI 10.1016/j.camwa.2004.03.002 | MR 2105244 | Zbl 1066.34019
[2] Chen, L., Sun, J.: Nonlinear boundary value problem of first order impulsive functional differential equations. J. Math. Anal. Appl. 318 (2006), 726-741. DOI 10.1016/j.jmaa.2005.08.012 | MR 2215181 | Zbl 1102.34052
[3] Ding, W., Han, M.: Periodic boundary value problem for the second order impulsive functional differential equations. Appl. Math. Comput. 155 (2004), 709-726. DOI 10.1016/S0096-3003(03)00811-7 | MR 2078208 | Zbl 1102.34324
[4] Kaufmann, E. R., Kosmatov, N., Raffoul, Y. N.: A second-order boundary value problem with impulsive effects on an unbounded domain. Nonlinear Anal., Theory Methods Appl. 69 (2008), 2924-2929. MR 2452102 | Zbl 1159.34023
[5] Lin, X., Jiang, D.: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations. J. Math. Anal. Appl. 321 (2006), 501-514. DOI 10.1016/j.jmaa.2005.07.076 | MR 2241134 | Zbl 1103.34015
[6] Lee, Y.-H., Liu, X.: Study of singular boundary value problems for second order impulsive differential equations. J. Math. Anal. Appl. 331 (2007), 159-176. DOI 10.1016/j.jmaa.2006.07.106 | MR 2305995 | Zbl 1120.34018
[7] Lee, E. K., Lee, Y.-H.: Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equation. Appl. Math. Comput. 158 (2004), 745-759. DOI 10.1016/j.amc.2003.10.013 | MR 2095700
[8] Rachůnková, I., Tomeček, J.: Singular Dirichlet problem for ordinary differential equation with impulses. Nonlinear Anal., Theory Methods Appl. 65 (2006), 210-229. DOI 10.1016/j.na.2005.09.016 | MR 2226265
[9] Rachůnková, I., Tvrdý, M.: Second-order periodic problem with $\varphi $-Laplacian and impulses. Nonlinear Anal., Theory Methods Appl. 63 (2005), 257-266. DOI 10.1016/j.na.2004.09.017
[10] Su, H., Wei, Z., Wang, B.: The existence of positive solutions for a nonlinear four-point singular boundary value problem with a $p$-Laplacian operator. Nonlinear Anal., Theory Methods Appl. 66 (2007), 2204-2217. MR 2311023 | Zbl 1126.34017
[11] Shen, J., Wang, W.: Impulsive boundary value problems with nonlinear boundary conditions. Nonlinear Anal., Theory Methods Appl. 69 (2008), 4055-4062. DOI 10.1016/j.na.2007.10.036 | MR 2463353 | Zbl 1171.34309
[12] Tian, Y., Jiang, D., Ge, W.: Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations. Appl. Math. Comput. 200 (2008), 123-132. DOI 10.1016/j.amc.2007.10.052 | MR 2421630 | Zbl 1156.34019
[13] Wang, Y., Hou, C.: Existence of multiple positive solutions for one dimensional $p$-Laplacian. J. Math. Anal. Appl. 315 (2006), 144-153. DOI 10.1016/j.jmaa.2005.09.085 | MR 2196536 | Zbl 1098.34017
[14] Zhang, X., Ge, W.: Impulsive boundary value problems involving the one-dimensional $p$-Laplacian. Nonlinear Anal., Theory Methods Appl. 70 (2009), 1692-1701. DOI 10.1016/j.na.2008.02.052 | MR 2483590 | Zbl 1183.34038
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