# zbMATH — the first resource for mathematics

Positive solutions for $$n$$th-order $$m$$-point $$p$$-Laplacian operator singular boundary value problems. (English) Zbl 1148.34019
Existence and multiplicity of positive solutions for a nonlinear $$n$$th-order $$m$$-point $$p$$-Laplacian singular boundary value problem are obtained by using the fixed-point index theory. The boundary value problems are transformed into integral equations by means of Green functions.

##### MSC:
 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations
Full Text:
##### References:
 [1] Wang, H.Y., On the existence of positive solutions for semilinear elliptic equations in the annulus, J. differ. equat., 109, 1-7, (1994) · Zbl 0798.34030 [2] Bandle, C.V.; Kwong, M.K., Semilinear elliptic problems in annular domains, J. appl. math. phys. ZAMP, 40, 245-257, (1989) · Zbl 0687.35036 [3] Wei, Z.L., Positive solutions of singular boundary value problems of negative exponent emden – fowler equations, Acts math. sinica, 41, 3, 653-662, (1998), (in Chinese) · Zbl 1027.34024 [4] Wei, Z.L., Positive solutions of singular Dirichlet boundary value problems, Chin. ann. math., 20(A), 543-552, (1999), (in Chinese) · Zbl 0948.34501 [5] Gatica, J.A.; Oliker, V.; Waltman, P., Singular boundary value problems for second order ordinary differential equation, J. differ. equat., 79, 62-78, (1989) · Zbl 0685.34017 [6] Ma, Y.Y., Positive solutions of singular second order boundary value problems, Acta math. sinica, 41, 6, 1225-1230, (1998), (in Chinese) · Zbl 1027.34025 [7] Kaufmann, E.R.; Kosmatov, N., A multiplicity result for a boundary value problem with infinitely many singularities, J. math. anal. appl., 269, 444-453, (2002) · Zbl 1011.34012 [8] Wong, F.H., The existence of positive solutions for m-Laplacian BVPs, Appl. math. lett., 12, 12-17, (1999) [9] He, X.M., The existence of positive solutions of p-Laplacian equation, Acta math. sinica, 46, 4, 805-810, (2003) · Zbl 1056.34033 [10] Liu, B., Positive solutions three-points boundary value problems for one-dimensional p-Laplacian with infinitely many singularities, Appl. math. lett., 17, 655-661, (2004) · Zbl 1060.34006 [11] Zhou, C.L.; Ma, D.X., Existence and iteration of positive solutions for a generalized right-focal boundary value problems with p-Laplacian operator, J. math. anal. appl., 324, 409-424, (2006) · Zbl 1115.34029 [12] Anderson, D.R., Green’s function for a third-order generalized right-focal problem, J. math. anal. appl., 288, 1-14, (2003) · Zbl 1045.34008 [13] Su, H.; Wei, Z.; Xu, F., The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator, J. math. anal. appl., 325, 319-332, (2007) · Zbl 1108.34015 [14] Su, H.; Wei, Z.; Xu, F., The existence of positive solutions for nonlinear singular boundary value system with p-Laplacian, J. appl. math. comp., 181, 826-836, (2006) · Zbl 1111.34020 [15] Pang, C.; Dong, W.; Wei, Z., Green’s function and positive solutions of nth order m-point boundary value problem, J. appl. math. comp., 182, 1231-1239, (2006) · Zbl 1111.34024 [16] Liu, Y.; Ge, W., Positive solutions for $$(n - 1, 1)$$ three-point boundary value problem with coefficient that changes sign, J. math. anal. appl., 282, 816-825, (2003) · Zbl 1033.34031 [17] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cone, (1988), Academic Press San Diego · Zbl 0661.47045 [18] Guo, D.; Lakshmikantham, V.; Liu, X., Nonlinear integral equations in abstract spaces, (1996), Kluwer Academic Publishers · Zbl 0866.45004 [19] Deimling, K., Nonlinear functional analysis, (1980), Springer-Verlag Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.