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SOLVABILITY OF ITERATIVE SYSTEMS OF THREE-POINT BOUNDARY VALUE PROBLEMS

Year 2013, Volume 3, Issue 2, 147 - 159, 01.12.2013

Abstract

We establish a criterion for the existence of at least one positive solution for the iterative system of three-point boundary value problems by determining the eigenvalues λi, 1 ≤ i ≤ n, using Guo–Krasnosel’skii fixed point theorem.

References

  • Agarwal, R. P., O’Regan, D. and Wong, P. J. Y., (1999), Positive solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht.
  • Erbe, L. H. and Wang, H., (1994), On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120, 743-748.
  • Fink, A. M. and Gatica, J. A., (1993), Positive solutions of second order systems of boundary value problem, J. Math. Anal. Appl., 180, 93-108.
  • Graef, J. R. and Yang, B., (2002), Boundary value problems for second order nonlinear ordinary differential equations, Comm. Appl. Anal., 6, 273-288.
  • Guo, D. and Lakshmikantham, V., (1988), Nonlinear Problems in Abstract Cones, Academic Press, Orlando.
  • Henderson, J. and Ntouyas, S. K., (2007), Positive solutions for systems of nth order three-point nonlocal boundary value problems, Elec. J. Qual. Theory Differ. Equ., 2007, No. 18, 1-12.
  • Henderson, J., Ntouyas, S. K. and Purnaras, I. K., (2008), Positive solutions for systems of generalized three-point nonlinear boundary value problems, Comment. Math. Univ. Carolin., 49, 79-91.
  • Henderson, J., Ntouyas, S. K. and Purnaras, I. K., (2008), Positive solutions for systems of second order four-point nonlinear boundary value problems, Comm. Appl. Anal., 12, No. 1, 29-40.
  • Henderson, J. and Wang, H., (1997), Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl., 208, 1051-1060.
  • Henderson, J. and Wang, H., (2005), Nonlinear eigenvalue problems for quasilinear systems, Comput. Math. Appl., 49, 1941-1949.
  • Henderson, J. and Wang, H., (2007), An eigenvalue problem for quasilinear systems, Rockey Mountain J. Math., 37, 215-228.
  • Hu, L. and Wang, L. L., (2007), Multiple positive solutions of boundary value problems for systems of nonlinear second order differential equations, J. Math. Anal. Appl., 335, 1052-1060.
  • Infante, G., (2003), Eigenvalues of some nonlocal boundary value problems, Proc. Edinburgh Math. Soc., 46, 75-86.
  • Ma, R., (2000), Multiplicity of nonnegative solutions of second order systems of boundary value problems, Nonlinear Anal., 42, 1003-1010.
  • Raffoul, Y., (2002), Positive solutions of three-point nonlinear second order boundary value problems
  • Elec. J. Qual. Theory Differ. Equ., 2002, No. 15, 1-11.
  • Wang, H., (2003), On the number of positive solutions of nonlinear systems, J. Math. Anal. Appl., , 287-306.
  • Webb, J. R. L., (2001), Positive solutions of some three-point boundary value problems via Şxed point index theory, Nonlinear Anal., 47 4319-4332.
  • Zhou, Y. and Xu, Y., (2006), Positive solutions of three-point boundary value problems for systems of nonlinear second order differential equations, J. Math. Anal. Appl., 320, 578-590.

Year 2013, Volume 3, Issue 2, 147 - 159, 01.12.2013

Abstract

References

  • Agarwal, R. P., O’Regan, D. and Wong, P. J. Y., (1999), Positive solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht.
  • Erbe, L. H. and Wang, H., (1994), On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120, 743-748.
  • Fink, A. M. and Gatica, J. A., (1993), Positive solutions of second order systems of boundary value problem, J. Math. Anal. Appl., 180, 93-108.
  • Graef, J. R. and Yang, B., (2002), Boundary value problems for second order nonlinear ordinary differential equations, Comm. Appl. Anal., 6, 273-288.
  • Guo, D. and Lakshmikantham, V., (1988), Nonlinear Problems in Abstract Cones, Academic Press, Orlando.
  • Henderson, J. and Ntouyas, S. K., (2007), Positive solutions for systems of nth order three-point nonlocal boundary value problems, Elec. J. Qual. Theory Differ. Equ., 2007, No. 18, 1-12.
  • Henderson, J., Ntouyas, S. K. and Purnaras, I. K., (2008), Positive solutions for systems of generalized three-point nonlinear boundary value problems, Comment. Math. Univ. Carolin., 49, 79-91.
  • Henderson, J., Ntouyas, S. K. and Purnaras, I. K., (2008), Positive solutions for systems of second order four-point nonlinear boundary value problems, Comm. Appl. Anal., 12, No. 1, 29-40.
  • Henderson, J. and Wang, H., (1997), Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl., 208, 1051-1060.
  • Henderson, J. and Wang, H., (2005), Nonlinear eigenvalue problems for quasilinear systems, Comput. Math. Appl., 49, 1941-1949.
  • Henderson, J. and Wang, H., (2007), An eigenvalue problem for quasilinear systems, Rockey Mountain J. Math., 37, 215-228.
  • Hu, L. and Wang, L. L., (2007), Multiple positive solutions of boundary value problems for systems of nonlinear second order differential equations, J. Math. Anal. Appl., 335, 1052-1060.
  • Infante, G., (2003), Eigenvalues of some nonlocal boundary value problems, Proc. Edinburgh Math. Soc., 46, 75-86.
  • Ma, R., (2000), Multiplicity of nonnegative solutions of second order systems of boundary value problems, Nonlinear Anal., 42, 1003-1010.
  • Raffoul, Y., (2002), Positive solutions of three-point nonlinear second order boundary value problems
  • Elec. J. Qual. Theory Differ. Equ., 2002, No. 15, 1-11.
  • Wang, H., (2003), On the number of positive solutions of nonlinear systems, J. Math. Anal. Appl., , 287-306.
  • Webb, J. R. L., (2001), Positive solutions of some three-point boundary value problems via Şxed point index theory, Nonlinear Anal., 47 4319-4332.
  • Zhou, Y. and Xu, Y., (2006), Positive solutions of three-point boundary value problems for systems of nonlinear second order differential equations, J. Math. Anal. Appl., 320, 578-590.

Details

Primary Language English
Journal Section Research Article
Authors

K.r. PRASAD This is me
Department of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India


N. SREEDHAR This is me
Department of Mathematics, GITAM University, Visakhapatnam, 530 045, India


K.r. KUMAR This is me
Department of Mathematics, VITAM College of Engineering, Visakhapatnam, 531 173, India

Publication Date December 1, 2013
Published in Issue Year 2013, Volume 3, Issue 2

Cite

Bibtex @ { twmsjaem761406, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {2}, pages = {147 - 159}, title = {SOLVABILITY OF ITERATIVE SYSTEMS OF THREE-POINT BOUNDARY VALUE PROBLEMS}, key = {cite}, author = {Prasad, K.r. and Sreedhar, N. and Kumar, K.r.} }