Positive solutions for systems of generalized three-point nonlinear boundary value problems

Johnny Henderson; Sotiris K. Ntouyas; Ioannis K. Purnaras

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 1, page 79-91
  • ISSN: 0010-2628

Abstract

top
Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u ' ' + λ a ( t ) f ( v ) = 0 , v ' ' + λ b ( t ) g ( u ) = 0 , for 0 < t < 1 , and satisfying, u ( 0 ) = β u ( η ) , u ( 1 ) = α u ( η ) , v ( 0 ) = β v ( η ) , v ( 1 ) = α v ( η ) . A Guo-Krasnosel’skii fixed point theorem is applied.

How to cite

top

Henderson, Johnny, Ntouyas, Sotiris K., and Purnaras, Ioannis K.. "Positive solutions for systems of generalized three-point nonlinear boundary value problems." Commentationes Mathematicae Universitatis Carolinae 49.1 (2008): 79-91. <http://eudml.org/doc/250464>.

@article{Henderson2008,
abstract = {Values of $\lambda $ are determined for which there exist positive solutions of the system of three-point boundary value problems, $u^\{\prime \prime \}+\lambda a(t) f(v) = 0$, $v^\{\prime \prime \}+\lambda b(t) g(u) = 0$, for $0 < t < 1$, and satisfying, $u(0) = \beta u(\eta )$, $u(1)=\alpha u(\eta )$, $v(0) = \beta v(\eta )$, $v(1) = \alpha v(\eta )$. A Guo-Krasnosel’skii fixed point theorem is applied.},
author = {Henderson, Johnny, Ntouyas, Sotiris K., Purnaras, Ioannis K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {generalized three-point boundary value problem; system of differential equations; eigenvalue problem; generalized three-point boundary value problem; system of differential equations; eigenvalue problem},
language = {eng},
number = {1},
pages = {79-91},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Positive solutions for systems of generalized three-point nonlinear boundary value problems},
url = {http://eudml.org/doc/250464},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Henderson, Johnny
AU - Ntouyas, Sotiris K.
AU - Purnaras, Ioannis K.
TI - Positive solutions for systems of generalized three-point nonlinear boundary value problems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 1
SP - 79
EP - 91
AB - Values of $\lambda $ are determined for which there exist positive solutions of the system of three-point boundary value problems, $u^{\prime \prime }+\lambda a(t) f(v) = 0$, $v^{\prime \prime }+\lambda b(t) g(u) = 0$, for $0 < t < 1$, and satisfying, $u(0) = \beta u(\eta )$, $u(1)=\alpha u(\eta )$, $v(0) = \beta v(\eta )$, $v(1) = \alpha v(\eta )$. A Guo-Krasnosel’skii fixed point theorem is applied.
LA - eng
KW - generalized three-point boundary value problem; system of differential equations; eigenvalue problem; generalized three-point boundary value problem; system of differential equations; eigenvalue problem
UR - http://eudml.org/doc/250464
ER -

References

top
  1. Agarwal R.P., O'Regan D., Wong P.J.Y., Positive Solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht, 1999. Zbl1157.34301
  2. Benchohra M., Hamani S., Henderson J., Ntouyas S.K., Ouahab A., Positive solutions for systems of nonlinear eigenvalue problems, Global J. Math. Anal. 1 (2007), 19-28. (2007) MR2374098
  3. Erbe L.H., Wang H., 10.1090/S0002-9939-1994-1204373-9, Proc. Amer. Math. Soc. 120 (1994), 743-748. (1994) Zbl0802.34018MR1204373DOI10.1090/S0002-9939-1994-1204373-9
  4. Graef J.R., Yang B., Boundary value problems for second order nonlinear ordinary differential equations, Commun. Appl. Anal. 6 (2002), 273-288. (2002) Zbl1085.34514MR1894171
  5. Guo D., Lakshmikantham V., Nonlinear Problems in Abstract Cones, Academic Press, Orlando, 1988. Zbl0661.47045MR0959889
  6. Henderson J., Ntouyas S.K., Positive solutions for systems of nonlinear boundary value problems, Nonlinear Studies, in press. Zbl1148.34016
  7. Henderson J., Ntouyas S.K., Positive solutions for systems of three-point nonlinear boundary value problems, Austr. J. Math. Anal. Appl., in press. MR2413225
  8. Henderson J., Wang H., 10.1006/jmaa.1997.5334, J. Math. Anal. Appl. 208 (1997), 1051-1060. (1997) Zbl0876.34023MR1440355DOI10.1006/jmaa.1997.5334
  9. Henderson J., Wang H., 10.1016/j.camwa.2003.08.015, Comput. Math. Appl. 49 (2005), 1941-1949. (2005) Zbl1092.34517MR2154696DOI10.1016/j.camwa.2003.08.015
  10. Henderson J., Wang H., 10.1216/rmjm/1181069327, Rocky Mountain J. Math. 37 (2007), 215-228. (2007) Zbl1149.34013MR2316445DOI10.1216/rmjm/1181069327
  11. Hu L., Wang L.L., 10.1016/j.jmaa.2006.11.031, J. Math. Anal. Appl. 335 (2007), 2 1052-1060. (2007) Zbl1127.34010MR2346890DOI10.1016/j.jmaa.2006.11.031
  12. Infante G., Eigenvalues of some nonlocal boundary value problems, Proc. Edinburgh Math. Soc. 46 (2003), 75-86. (2003) MR1961173
  13. Infante G., Webb J.R.L., 10.1007/s00030-005-0039-y, Nonlinear Differential Equations Appl. 13 (2006), 249-261. (2006) Zbl1112.34017MR2243714DOI10.1007/s00030-005-0039-y
  14. Liang R., Peng J., Shen J., Positive solutions to a generalized second order three-point boundary value problem, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.025. Zbl1140.34313
  15. Ma R., 10.1016/S0362-546X(99)00152-2, Nonlinear Anal. 42 (2000), 1003-1010. (2000) Zbl0973.34014MR1780450DOI10.1016/S0362-546X(99)00152-2
  16. Raffoul Y., Positive solutions of three-point nonlinear second order boundary value problems, Electron. J. Qual. Theory Differ. Equ. 2002, no. 15, 11pp. (electronic). MR1934391
  17. Wang H., 10.1016/S0022-247X(03)00100-8, J. Math. Anal. Appl. 281 (2003), 287-306. (2003) Zbl1036.34032MR1980092DOI10.1016/S0022-247X(03)00100-8
  18. Webb J.R.L., 10.1016/S0362-546X(01)00547-8, Nonlinear Anal. 47 (2001), 4319-4332. (2001) Zbl1042.34527MR1975828DOI10.1016/S0362-546X(01)00547-8
  19. Zhou Y., Xu Y., 10.1016/j.jmaa.2005.07.014, J. Math. Anal. Appl. 320 (2006), 578-590. (2006) Zbl1101.34008MR2225977DOI10.1016/j.jmaa.2005.07.014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.