SOLVABILITY OF ITERATIVE SYSTEMS OF THREE-POINT BOUNDARY VALUE PROBLEMS
Year 2013,
Volume 3,
Issue 2,
147 - 159,
01.12.2013
K.r. PRASAD
N. SREEDHAR
K.r. KUMAR
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
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- 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
K.r. PRASAD
N. SREEDHAR
K.r. KUMAR
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.