REFERENCES
[1] P. Binding, P. Dr´abek, Sturm-Liouville theory for the p-Laplacian, Studia Sci. Math. Hungar.
40 (2003), 375–396.
[2] C. Bai, J. Fang, Existence of multiple positive solutions for nonlinear m-point boundary value
problems, J. Math. Anal. Appl. 281 (2003), 76–85.
[3] E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New
York, 1955.
[4] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
[5] N. Dodds, B. P. Rynne, Spectral properties and nodal solutions for second-order, m-point,
p-Laplacian boundary value problems, Topol. Methods Nonlinear Anal. 32 (2008), 21–40.
[6] J. Gao, D. Sun, M. Zhang, Structure of Eigenvalues of Multi-point Boundary Value Problems,
preprint.
[7] M. Garc´ıa-Huidobro, Ch. P. Gupta, R. Man´asevich, Some multipoint boundary value problems
of Neumann-Dirichlet type involving a multipoint p-Laplace like operator, J. Math. Anal. Appl.
333 (2007), 247–264.
[8] M. Garc´ıa-Huidobro, R. Man´asevich, J. R. Ward, A homotopy along p for systems with a
p-Laplace operator, Adv. Differential Equations 8 (2003), 337–356.
[9] C. P. Gupta, A non-resonant generalized multi-point boundary-value problem of Dirichelet
type involving a p-Laplacian type operator, in: Proceedings of the Sixth Mississippi State–UBA
Conference on Differential Equations and Computational Simulations, 127–139, Electron. J.
Differ. Equ. Conf., 15, Southwest Texas State Univ., San Marcos, TX, 2007.
[10] E. Hewitt, K. Stromberg, Real and Abstract Analysis, Second Edition, Springer, 1969.
[11] Y. X. Huang, G. Metzen, The existence of solutions to a class of semilinear differential equations,
Differential Integral Equations 8 (1995), 429–452.
[12] A. N. Kolmogorov, S. V. Fomin, Introductory Real Analysis, Dover, New York, 1975.
[13] P. Lindqvist, Some remarkable sine and cosine functions, Ricerche di Matematica 44 (1995),
269–290.
[14] Y. Liu, Non-homogeneous boundary-value problems of higher order differential equations with
p-Laplacian, Electron. J. Differential Equations 2008, No. 22.
[15] R. Ma, D. O’Regan, Nodal solutions for second-order m-point boundary value problems with
nonlinearities across several eigenvalues, Nonlinear Anal. 64 (2006), 1562–1577.
[16] P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Analysis 7
(1971), 487-513
[17] B. P. Rynne, Spectral properties and nodal solutions for second-order, m-point, boundary
value problems, Nonlinear Analysis 67 (2007), 3318–3327.
[18] B. P. Rynne, Spectral properties of second-order, multi-point, p-Laplacian boundary value
problems, Nonlinear Analysis 72 (2010), 4244–4253.
[19] B. P. Rynne, Spectral properties of p-Laplacian problems with Neumann and mixed-type
multi-point boundary conditions, Nonlinear Analysis 74 (2010), 1471–1484.
[20] B. P. Rynne, Eigenvalue criteria for existence of positive solutions of second-order, multi-point,
p-Laplacian boundary value problems, Topol. Methods Nonlinear Anal. 36 (2010), 311–326.
[21] J. R. L. Webb, G. Infante, Positive solutions of nonlocal boundary value problems: a unified
approach, J. London Math. Soc. 74 (2006), 673–693.
[22] J. R. L. Webb, K. Q. Lan, Eigenvalue criteria for existence of multiple positive solutions of
nonlinear boundary value problems of local and nonlocal type, Topol. Methods Nonlinear Anal.
27 (2006), 91–115.
[23] X. Xu, Multiple sign-changing solutions for some m-point boundary-value problems, Electron.
J. Differential Equations 89 (2004).
[24] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. I - Fixed Point Theorems,
Springer-Verlag, New York, 1986.