Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem
Commenced in January 2007
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Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem

Authors: Benshi Zhu

Abstract:

In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082127

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[1] R.P. Agarwal, Difference equations and inequalities, in: Monographs and Textbooks in Pure and Applied Mathematics, Vol. 228, Marcel Dekker Inc. New York, 2000.
[2] Gabriele Bonannoa, Pasquale Candito, "Nonlinear difference equations investigated via critical point methods", Nonlinear Anal., Vol. 70, pp. 3180-3186, May 2009.
[3] G. Bonanno, P. Candito, "On a class of nonlinear variationalhemivariational inequalities", Appl. Anal. Vol.83, pp. 1229-1244, Dec. 2004.
[4] G. Bonanno, N. Giovannelli, "An eigenvalue Dirichlet problem involving the p-Laplican with discontinuous nonlinearities", J. Math. Anal. Appl. Vol.308, pp. 596-604, Aug. 2005.
[5] A. Castro, R.Shivaji, "Nonnegative solutions for a class of nonpositone problems", Proc. Roy. Soc. Edin. Vol. 108A, pp. 291-302, 1988.
[6] K.C. Chang, "Variational methods for non-differential functional and their applications to PDE", J. Math. Anal. Appl. Vol. 80, pp. 102-129, Mar. 1981.
[7] A. Castro, C. Maya, R.Shivaji, "Nonlinear eigenvalue problems with semipositone structure", Electronic J. Diff. Eqns. Conference 05, pp. 33-49, 2000.
[8] D.S. Cohn, H.B. Keller, "Some positone problems suggested by nonlinear heat generation", J. Math. Mech. Vol. 16, pp. 1361-1376, June 1967.
[9] D.G. Costa, H. Tehrani, J. Yang, "On a variational approach to existence and multiplicity results for semipositone problems", Electronic J. Diff. Eqns. vol. 2000, pp. 1-10, 2000.
[10] B. Ricceri, "On a three critical points theorem", Arch. Math. (Basel) Vol. 75, pp. 220-226, 2000.
[11] Biagio Ricceri, "A three critical points theorem revisited", Nonlinear Anal. Vol. 70, pp. 3084-3089, May 2009.
[12] G. Zhang, S. Liu, On a class of semipositone discrete boundary value problems, J. Math. Anal. Appl. Vol. 325, pp175-182, Jan. 2007.