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Existence and multiplications of solutions for a class of equation with a non-smooth potential | ||
| Journal of Hyperstructures | ||
| دوره 4، شماره 2، اسفند 2015، صفحه 170-183 اصل مقاله (129.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2015.2607 | ||
| نویسندگان | ||
| Fariba Fattahi* 1؛ M. Alimohammady2 | ||
| 1Department of Mathematics, University of Mazandaran, Babolsar, IRAN | ||
| 2Department of Mathematics, University of Mazandaran, P.O.Box 47416-1468, Babolsar, Iran | ||
| چکیده | ||
| This paper deals with the existence and multiplicity of solutions for a class of nonlocal p−Kirchhoff problem. Using the mountain pass theorem and fountain theorem, we establish the existence of at least one solution and infinitely many solutions for a class of locally Lipschitz functional. | ||
| کلیدواژه‌ها | ||
| p-Kirichhoff problem؛ Symmetric Mountain Pass theorem؛ fountain theorem؛ hemivariational inequality | ||
| مراجع | ||
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[1] M. Alimohammady, F. Fattahi, Existence of solutions to hemivaritional inequal-ities involving the p(x)-biharmonic operator, Electron. J. Diff. Equ., Vol. 2015(2015), 1-12. [2] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381. [3] G. Bonannoa, P. Winkert, Multiplicity results to a class of variational-hemivariational inequalities, Topological methods in nonlinear analysis,43(2)(2014), 493-516. [4] F. H. Clarke, Optimization and nonsmooth analysis, John Wiley & Sons, New York, 1983. [5] J. Chabrowski, Variational Methods for Potential Operator Equations, de Gruyter, 1997. [6] N. Costea, C. Varga, Multiple critical points for non-differentiable parametrized functionals and applications to differential inclusions, Journal of Global Opti-mization, vol. 56 (2013), 399-416. [7] G. Dai, Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem, Nonlinear Anal. 72 (2010), 1454-1461. doi:10.1016/j.na.2009.08.029 [8] O. Frites , T. Moussaoui, Existence of positive solutions for a variational in-equality of Kirchhoff type, Arab Journal of Mathematical Sciences, 21(2) (2015),127-135. [9] Sh. Heidarkhani, J. Chu, F. Gharehgazlouei, A. Solimaninia, Three nontrivial solutions for Kirchhoff-type variational-hemivariational inequalities, Results in Mathematics, 68 (2015), 71-91. [10] G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883. [11] G. Sun, K. Teng, Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem, Math. Commun. 183 19 (2014), 183-194. [12] M. C. Wei, C. L. Tang, Existence and Multiplicity of Solutions for p(x)-Kirchhoff-Type Problem in R N , Bull. Malays. Math. Sci. Soc. (2) 36(3) (2013), 767-781. [13] P. Winkert, On the Boundedness of Solutions to Elliptic Variational Inequalities,Set-Valued and Var. Anal. 22(4) 2014, 763-781., DOI:10.1007/s11228-014-0281-8. [14] Q. L. Xie, X. P. Wu, C.-L. Tang, Existence of solutions for Kirchhoff type equations, Electronic Journal of Differential Equations, Vol. 2015 (2015), 1-8. [15] M. Xiang, A variational inequality involving nonlocal elliptic operators, Fixed Point Theory and Applications, (2015), 1-9. doi:10.1186/s13663-015-0394-2 [16] Z. Yuan, L. Huang, Existence of solutions for p(x)−Kirchhoff type problems with non-smooth potentials, Electronic Journal of Differential Equations, Vol. 2015(2015), 1-18. | ||
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