Abstract
In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).
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Feng, H., Ge, W.: Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional p-Laplacian. Math. Comput. Modell. 47, 186–195 (2008)
Feng, H., Ge, W.: Existence of three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian. Nonlinear Anal. 68, 2017–2026 (2008)
Fenga, H., Ge, W., Jiang, M.: Multiple positive solutions for m-point boundary-value problems with a one-dimensional p-Laplacian. Nonlinear Anal. 68, 2269–2279 (2008)
Feng, W., Webb, J.R.L.: Solvability of m-point boundary value problem with nonlinear growth. J. Math. Appl. 212, 467–480 (1997)
Graef, J.R., Yang, B.: Positive solutions to a multi-point higher order boundary value problem. J. Math. Anal. Appl. 316, 409–421 (2006)
Guo, Y., Ji, Y., Liu, X.: Multiple positive solutions for some multi-point boundary value problems with p-Laplacian. J. Comput. Appl. Math. 216, 144–156 (2008)
Gupta, C.P.: A generalized multi-point boundary value problem for second order ordinary differential equation. Appl. Math. Comput. 89, 138–146 (1998)
Jiang, W.: Multiple positive solutions for nth-order m-point boundary value problems with all derivatives. Nonlinear Anal. 68, 1064–1072 (2008)
Ma, R., O’Regan, D.: Solvability of singular second order m-point boundary value problems. J. Math. Appl. 301, 124–134 (2005)
Pang, C., Dong, W., Wei, Z.: Green’s function and positive solutions of nth order m-point boundary value problem. Appl. Math. Comput. 182, 1231–1239 (2006)
O’Regan, D.: Theory of Singular Boundary Value Problems. World Scientific, Singapore (1994)
O’Regan, D.: Singular Dirichlet boundary value problems—I. Super-linear and non-resonance case. Nonlinear Anal. TMA 29(2), 221–245 (1997)
Su, H.: Positive solutions for n-order m-point p-Laplacian operator singular boundary value problems. Appl. Math. Comput. 199, 122–132 (2008)
Sun, B., Qu, Y., Ge, W.G.: Existence and iteration of positive solutions for a multipoint one-dimensional p-Laplacian boundary value problem. Appl. Math. Comput. 197, 389–398 (2008)
Taliaferro, S.D.: A nonlinear singular boundary value problem. Nonlinear Anal. TMA 3, 897–904 (1979)
Wei, Z., Pang, C.: Positive solutions of non-resonant singular boundary value problem of second order differential equations. Nagoya Math. J. 162, 127–148 (2001)
Wei, Z.: A class of fourth order singular boundary value problems. Appl. Math. Comput. V 153(3), 865–884 (2004)
Zhang, Y.: Positive solutions of singular sub-linear Emden–Fowler boundary value problems. J. Math. Anal. Appl. 185, 215–222 (1994)
Zhang, G., Sun, J.: Positive solutions of m-point boundary value problem. J. Math. Anal. Appl. 291, 406–418 (2004)
Zhu, Y., Wang, K.: On the existence of solutions of p-Laplacian m-point boundary value problem at resonance. Nonlinear Anal. 70, 1557–1564 (2009)
Guo, D.J.: Nonlinear Functional Analysis. Shandong Sci. and Tech. Press, Jinan (1985) (in Chinese)
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This work was supported by the NNSF of China (10671167,10771212).
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Zhu, Y., Zhu, J. Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems. J. Appl. Math. Comput. 34, 393–405 (2010). https://doi.org/10.1007/s12190-009-0329-3
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DOI: https://doi.org/10.1007/s12190-009-0329-3