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Abstrakty
In this paper, we establish the existence of at least three solutions of the multi-point boundary value system [formula]. The approaches used are based on variational methods and critical point theory.
Czasopismo
Rocznik
Tom
Strony
293--306
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- University of Tennessee at Chattanooga Department of Mathematics Chattanooga, TN 37403, USA
autor
- Razi University Faculty of Sciences Department of Mathematics Kermanshah 67149, Iran
- Institute for Research in Fundamental Sciences (IPM) School of Mathematics P.O. Box 19395-5746, Tehran, Iran
autor
- Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA
Bibliografia
- [1] D. Averna, G. Bonanno, A mountain pass theorem for a suitable class of functions. Rocky Mountain J. Math. 39 (2009), 707-727.
- [2] D. Averna, G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal. 22 (2003), 93-103.
- [3] G. Bonanno, A critical point theorem via the Ekeland variational principle, Nonlinear Anal. 75 (2012), 2992-3007.
- [4] G. Bonanno, G. Molica Bisci, Three weak solutions for elliptic Dirichlet problems, J. Math. Anal. Appl. 382 (2011), 1-8.
- [5] G. Bonanno, G. Molica Bisci, V. Radulescu, Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz-Sobolev spaces, Monatsh. Math. 165 (2012), 305-318.
- [6] G. Bonanno, P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations 244 (2008), 3031-3059.
- [7] Z. Du, L. Kong, Existence of three solutions for systems of multi-point boundary value problems, Electron. J. Qual. Theory Diff. Equ., Spec. Ed. I, 10 (2009), 17 pp.
- [8] P.W. Eloe, B. Ahmad, Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions, Appl. Math. Lett. 18 (2005), 521-527.
- [9] H. Feng, W. Ge, Existence of three positive solutions for M-point boundary-value problem with one-dimensional P-Laplacian, Taiwanese J. Math. 14 (2010), 647-665.
- [10] W. Feng, J.R.L. Webb, Solvability of m-point boundary value problems with nonlinear growth, J. Math. Anal. Appl. 212 (1997), 467-480.
- [11] J.R. Graef, S. Heidarkhani, L. Kong, A critical points approach to multiplicity results for multi-point boundary value problems, Appl. Anal. 90 (2011), 1909-1925.
- [12] J.R. Graef, S. Heidarkhani, L. Kong, Infinitely many solutions for systems of multi-point boundary value problems, Topol. Methods Nonlinear Anal., to appear.
- [13] J.R. Graef, L. Kong, Existence of solutions for nonlinear boundary value problems, Comm. Appl. Nonlinear Anal. 14 (2007), 39-60.
- [14] J.R. Graef, L. Kong, Q. Kong, Higher order multi-point boundary value problems, Math. Nachr. 284 (2011), 39-52.
- [15] S. Heidarkhani, Multiple solutions for a class of multipoint boundary value systems driven by a one dimensional (pi,... ,pn)-Laplacian operator, Abstract Appl. Anal. 2012 (2012), Article ID 389530, 15 pp.
- [16] J. Henderson, Solutions of multipoint boundary value problems for second order equations, Dynam. Systems Appl. 15 (2006), 111-117.
- [17] J. Henderson, B. Karna, C.C. Tisdell, Existence of solutions for three-point boundary value problems for second order equations, Proc. Amer. Math. Soc. 133 (2005), 1365-1369.
- [18] J. Henderson, S.K. Ntouyas, Positive solutions for systems of nth order three-point nonlocal boundary value problems, Electron. J. Qual. Theory Diff. Equ. 18 (2007), 12 pp. (electronic).
- [19] R. Ma, Existence of positive solutions for superlinear m-point boundary value problems, Proc. Edinb. Math. Soc. 46 (2003), 279-292.
- [20] D. Ma, X. Chen, Existence and iteration of positive solutions for a multi-point boundary value problem with a p-Lapladan operator, Portugal. Math. (N. S.) 65 (2008), 67-80.
- [21] R. Ma, D. O'Regan, Solvability of singular second order m-point boundary value problems, J. Math. Anal. Appl. 301 (2005), 124-134.
- [22] G. Molica Bisci, D. Repovs, Nonlinear algebraic systems with discontinuous terms, J. Math. Anal. Appl. 398 (2013), 846-856.
- [23] B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401-410.
- [24] E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II., New York 1985.
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Bibliografia
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