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2014 | 12 | 10 | 1403-1415
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Three solutions to discrete anisotropic problems with two parameters

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Języki publikacji
EN
Abstrakty
EN
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
10
Strony
1403-1415
Opis fizyczny
Daty
wydano
2014-10-01
online
2014-06-21
Twórcy
Bibliografia
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  • [4] G. Molica Bisci and G. Bonanno. Three weak solutions for elliptic dirichlet problems. J. Math. Anal. Appl., 382:1–8, 2011. http://dx.doi.org/10.1016/j.jmaa.2011.04.026
  • [5] G. Bonanno. A minimax inequality and its applications to ordinary differential equations. J. Math. Anal. Appl, 270:210–229, 2002. http://dx.doi.org/10.1016/S0022-247X(02)00068-9
  • [6] G. Bonanno and A. Chinně. Existence of three solutions for a perturbed two-point boundary value problem. Appl. Math. Lett., 23(7):807–811, 2010. http://dx.doi.org/10.1016/j.aml.2010.03.015
  • [7] A. Cabada and A. Iannizzotto. A note on a question of ricceri. Appl. Math. Lett., 25:215–219, 2012. http://dx.doi.org/10.1016/j.aml.2011.08.024
  • [8] A. Cabada, A. Iannizzotto, and S. Tersian. Multiple solutions for discrete boundary value problems. J. Math. Anal. Appl., 356(2):418–428, 2009. http://dx.doi.org/10.1016/j.jmaa.2009.02.038
  • [9] X. Cai and J. Yu. Existence theorems of periodic solutions for second-order nonlinear difference equations. Adv. Difference Equ., 2008.
  • [10] Y. Chen, S. Levine, and M. Rao. Variable exponent, linear growth functionals in image processing. SIAM J. Appl. Math., 66(4):1383–1406, 2006. http://dx.doi.org/10.1137/050624522
  • [11] X.L. Fan and H. Zhang. Existence of solutions for p(x)-laplacian Dirichlet problem. Nonlinear Anal. Theory Methods Appl., 2003.
  • [12] M. Galewski and R. Wieteska. A note on the multiplicity of solutions to anisotropic discrete BVP’s. Appl. Math. Lett., 26:524–529, 2012. http://dx.doi.org/10.1016/j.aml.2012.11.002
  • [13] P. Harjulehto, P. Hästö, U. V. Le, and M. Nuortio. Overview of differential equations with non-standard growth. Nonlinear Anal., 72:4551–4574, 2010. http://dx.doi.org/10.1016/j.na.2010.02.033
  • [14] B. Kone and S. Ouaro. Weak solutions for anisotropic discrete boundary value problems. J. Difference Equ. Appl., 17:1537–1547, 2011. http://dx.doi.org/10.1080/10236191003657246
  • [15] J.Q. Liu and J.B. Su. Remarks on multiple nontrivial solutions for quasi-linear resonant problemes. J. Math. Anal. Appl., 258:209–222, 2001. http://dx.doi.org/10.1006/jmaa.2000.7374
  • [16] M. Mihǎilescu, V. Rǎdulescu, and S. Tersian. Eigenvalue problems for anisotropic discrete boundary value problems. J. Difference Equ. Appl., 15(6):557–567, 2009. http://dx.doi.org/10.1080/10236190802214977
  • [17] B. Ricceri. A general variational principle and some of its applications. J. Comput. Appl. Math., 113:401–410, 2000. http://dx.doi.org/10.1016/S0377-0427(99)00269-1
  • [18] B. Ricceri. On a three critical points theorem. Arch. Math. (Basel), 75:220–226, 2000. http://dx.doi.org/10.1007/s000130050496
  • [19] B. Ricceri. A further three critical points theorem. Nonlinear Anal., 2009.
  • [20] B. Ricceri. A three critical points theorem revisited. Nonlinear Anal., 70:3084–3089, 2009. http://dx.doi.org/10.1016/j.na.2008.04.010
  • [21] B. Ricceri. A further refinement of a three critical points theorem. Nonlinear Anal., 74(18):7446–7454, 2011. http://dx.doi.org/10.1016/j.na.2011.07.064
  • [22] M. Růžička. Electrorheological fluids: Modelling and mathematical theory. Lecture Notes in Mathematics, 1748, 2000.
  • [23] J. Zhang Y. Yang. Existence of solution for some discrete value problems with a parameter. Appl. Math. Comput., 211:293–302, 2009. http://dx.doi.org/10.1016/j.amc.2009.01.040
  • [24] G. Zhang. Existence of non-zero solutions for a nonlinear system with a parameter. Nonlinear Anal., 66(6):1400–1416, 2007. http://dx.doi.org/10.1016/j.na.2006.01.024
  • [25] G. Zhang and S.S. Cheng. Existence of solutions for a nonlinear system with a parameter. J. Math. Anal. Appl., 314(1):311–319, 2006. http://dx.doi.org/10.1016/j.jmaa.2005.03.098
  • [26] V.V. Zhikov. Averaging of functionals of the calculus of variations and elasticity theory. Math. USSR Izv., 29:33–66, 1987. http://dx.doi.org/10.1070/IM1987v029n01ABEH000958
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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