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2011 | 9 | 5 | 1156-1163
Tytuł artykułu

Positivity conditions and bounds for Green’s functions for higher order two-point BVP

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1156-1163
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
Twórcy
Bibliografia
  • [1] Agarwal R.P., O’Regan D., Ordinary and Partial Differential Equations, Universitext, Springer, New York, 2009
  • [2] Agarwal R.P., O’Regan D., Wong P.J.Y., Positive Solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht, 1999
  • [3] Bai Z., W. Ge, Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives, J. Math. Anal. Appl., 2003, 279(2), 442–450 http://dx.doi.org/10.1016/S0022-247X(03)00011-8
  • [4] Chen Y.S., The singular perturbation of two-point boundary value problem for nonlinear systems, Ann. Differential Equations, 1995, 10(5), 18–21
  • [5] Eloe P.W., Henderson J., Positive solutions for higher order ordinary differential equations, Electron. J. Differential Equations, 1995, #3
  • [6] Gil’ M.I., Positive solutions of equations with nonlinear causal mappings, Positivity, 2007, 11(3), 523–535 http://dx.doi.org/10.1007/s11117-007-2076-8
  • [7] Gil’ M.I., Positivity of the Green functions for higher order ordinary differential equations, Electron. J. Differential Equations, 2008, #97
  • [8] Gil’ M.I., Two sided bounds and positivity conditions for the Green function to periodic problem for a higher order ODE, Int. J. Dyn. Syst. Differ. Equ., 2009, 2(3–4), 253–261
  • [9] Guo Y., Gao Y., The method of upper and lower solutions for a Lidstone boundary value problem, Czechoslovak Math. J., 2005, 55(130) (3), 639–652 http://dx.doi.org/10.1007/s10587-005-0051-8
  • [10] Jódar L., Villanueva R.J., Navarro E., Solving nonmonic higher order two-point boundary value matrix problems using quasi-Green’s matrix functions, Analysis, 1992, 12(1–2), 139–157
  • [11] Krasnosel’skii M.A., Burd V.Sh., Kolesov Yu.S., Nonlinear Almost Periodic Oscillations, Nauka, Moscow, 1970 (in Russian)
  • [12] Krasnosel’skii M.A., Zabreiko P.P., Geometric Methods of Nonlinear Analysis, Nauka, Moscow, 1975 (in Russian)
  • [13] Kusano T., Naito M., Unbounded nonoscillatory solutions of nonlinear ordinary differential equations of arbitrary order, Hiroshima Math. J., 1988, 18(2), 361–372
  • [14] Laptinsky V.N., Makovetsky I.I., On the two-point boundary-value problem for the Riccati matrix differential equation, Cent. Eur. J. Math., 2005, 3(1), 143–154 http://dx.doi.org/10.2478/BF02475661
  • [15] Murty K.N., Sarma G.V.R.L., Theory of differential inequalities for two-point boundary value problems and their applications to three-point B.V.Ps associated with nth order non-linear system of differential equations, Appl. Anal., 2002, 81(1), 39–49 http://dx.doi.org/10.1080/0003681021000021051
  • [16] Murty M.S.N., Apparao B.V., Two point boundary value problems for matrix differential equations, J. Indian Math. Soc., 2006, 73(1–2), 1–7
  • [17] Nagle R.K., Saff E.B., Snider A.D., Fundamentals of Differential Equations and Boundary Value Problems, Addison-Wesley, New York, 1996
  • [18] Naito M., Yano K., Positive solutions of higher order ordinary differential equations with general nonlinearities, J. Math. Anal. Appl., 2000, 250(1), 27–48 http://dx.doi.org/10.1006/jmaa.2000.6953
  • [19] Wang Y.-M., On 2nth-order Lidstone boundary value problems, J. Math. Anal. Appl., 2005, 312(2), 383–400 http://dx.doi.org/10.1016/j.jmaa.2005.03.039
  • [20] Yao Q., Positive solutions to a semilinear system of second-order two-point boundary value problems, Ann. Differential Equations, 2006, 22(1), 87–94
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0052-9
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