Abstract
We study the existence of positive solutions for a higher-order nonlinear differential system subject to some m-point boundary conditions. As applications of the main results, we present two existence theorems for the positive solutions of a higher-order nonlinear differential equation with boundary conditions of the same form as those for the studied system.
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Anderson D.R.: Solutions to second-order three-point problems on time scales. J. Difference Equ. Appl. 8, 673–688 (2002)
Anderson D.R.: Twin n-point boundary value problems. Appl. Math. Lett. 17, 1053–1059 (2004)
Cheung W., Ren J.: Positive solutions for discrete three-point boundary value problems. Aust. J. Math. Anal. Appl. 1, 1–7 (2004)
Eloe P.W., Henderson J.: Positive solutions for (n - 1, 1) conjugate boundary value problems. Nonlinear Anal. 28, 1669–1680 (1997)
Ge W., Xue C.: Some fixed point theorems and existence of positive solutions of two-point boundary-value problems. Nonlinear Anal. 70, 16–31 (2009)
Graef J.R., Henderson J., Yang B.: Positive solutions of a nonlinear higher order boundary-value problem. Electron. J. Differential Equations 2007(45), 1–10 (2007)
Guo Y., Shan W., Ge W.: Positive solutions for second order m-point boundary value problems. J. Comput. Appl. Math. 151, 415–424 (2003)
Henderson J., Ntouyas S.K.: Positive solutions for systems of nth order threepoint nonlocal boundary value problems. Electron. J. Qual. Theory Differ. Equ. 2007(18), 1–12 (2007)
Henderson J., Ntouyas S.K.: Positive solutions for systems of nonlinear boundary value problems. Nonlinear Stud. 15, 51–60 (2008)
Henderson J., Ntouyas S.K.: Positive solutions for systems of three-point nonlinear boundary value problems. Aust. J. Math. Anal. Appl. 5, 1–9 (2008)
Henderson J., Ntouyas S.K., Purnaras I.K.: Positive solutions for systems of three-point nonlinear discrete boundary value problems. Neural Parallel Sci. Comput. 16, 209–224 (2008)
Henderson J., Ntouyas S.K., Purnaras I.: Positive solutions for systems of generalized three-point nonlinear boundary value problems. Comment. Math. Univ. Carolin. 49, 79–91 (2008)
Henderson J., Ntouyas S.K., Purnaras I.K.: Positive solutions for systems of nonlinear discrete boundary value problems. J. Difference Equ. Appl. 15, 895–912 (2009)
Il’in V., Moiseev E.: Nonlocal boundary value problems of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differ. Equ. 23, 803–810 (1987)
Il’in V.A., Moiseev E.I.: Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator. Differ. Equ. 23, 979–987 (1987)
Ji Y., Guo Y., Yu C.: Positive solutions to (n − 1, n) m-point boundary value problemss with dependence on the first order derivative. Appl. Math. Mech. (English Ed.) 30, 527–536 (2009)
Li W.T., Sun H.R.: Positive solutions for second-order m-point boundary value problems on times scales. Acta Math. Sin. (Engl. Ser.) 22, 1797–1804 (2006)
R., Luca Existence of positive solutions for a discrete boundary value problem. Istanbul Univ. Fen Fak. Mat. Fiz. Astron. Derg. (New Ser.) 3 (2008-2009), 119–126.
Luca R.: Positive solutions for m + 1-point discrete boundary value problems. Libertas Math. XXIX, 65–82 (2009)
Luca R.: Existence of positive solutions for a class of higher-order m-point boundary value problems. Electron. J. Qual. Theory Diff. Equ. 2010(74), 1–15 (2010)
R., Luca, Positive solutions for a second-order m-point boundary value problems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., in press.
R. Luca, On a class of m-point boundary value problems. Math. Bohem., in press.
Ma R.: Positive solutions of a nonlinear three point boundary value problem. Electron. J. Differential Equations 1999(34), 1–8 (1999)
Ma R.: Positive solutions for second order three-point boundary value problems. Appl. Math. Lett. 14, 1–5 (2001)
Ma R.: Existence of positive solutions for the symmetry three-point boundary value problem. Electron. J. Differential Equations 2007(154), 1–8 (2007)
Ma R., Raffoul Y.: Positive solutions of three-point nonlinear discrete second order boundary value problem. J. Difference Equ. Appl. 10, 129–138 (2004)
Moshinsky M.: Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas. Bol. Soc. Mat. Mexicana 7, 1–25 (1950)
S.K. Ntouyas, Nonlocal initial and boundary value problems: a survey, Handbook of differential equations: Ordinary differential equations. Vol.II, 461-557, Elsevier, Amsterdam, 2005.
Su H., Wei Z., Zhang X., Liu J.: Positive solutions of n-order and m-order multi-point singular boundary value system. Appl. Math. Comput. 188, 1234–1243 (2007)
Sun H.R., Li W.T.: Existence of positive solutions for nonlinear three-point boundary value problems on time scales. J. Math. Anal. Appl. 299, 508–524 (2004)
Timoshenko S.: Theory of elastic stability. McGraw-Hill, New York (1961)
Webb J.R.L.: Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Anal. 47, 4319–4332 (2001)
Webb J.R.L.: Nonlocal conjugate type boundary value problems of higher order. Nonlinear Anal. 71, 1933–1940 (2009)
Zhou Y., Xu Y.: Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations. J. Math. Anal. Appl. 320, 578–590 (2006)
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Luca, R. Positive Solutions for a Higher-Order m-Point Boundary Value Problem. Mediterr. J. Math. 9, 379–392 (2012). https://doi.org/10.1007/s00009-011-0125-9
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DOI: https://doi.org/10.1007/s00009-011-0125-9