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On a class of $l(x)$-biharmonic Kirchhoff-type problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 29 مهر 1404 اصل مقاله (384.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34439.5145 | ||
| نویسنده | ||
| Maryam Mirzapour* | ||
| Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran | ||
| تاریخ دریافت: 24 خرداد 1403، تاریخ بازنگری: 02 مرداد 1403، تاریخ پذیرش: 29 مرداد 1403 | ||
| چکیده | ||
| In this paper we deal with the multiplicity of solutions for the following Kirchhoff-type problem with Navier-boundary conditions \begin{equation*} \begin{gathered} \mathcal{K} \Big (\int_{\Lambda}\frac{1}{l(\chi)}|\Delta \varphi|^{l(\chi)}d\chi\Big) \Delta (|\Delta \varphi|^{l(\chi)-2}\Delta \varphi)=\theta |\varphi|^{r(\chi)-2}\varphi +\eta |\varphi|^{t(\chi)-2}\varphi \quad \text{in } \Lambda,\\ \varphi =\Delta \varphi =0 \quad \text{on } \partial\Lambda. \end{gathered} \end{equation*} where $\Lambda$ is a bounded domain in $\mathbb{R}^{N}$ and its boundary $\partial \Lambda$, is smooth , and $\mathcal{K} $ is a continuous Kirchhoff-type function, $l(\chi),r(\chi)$ and $t(\chi)$ are continuous functions on $\overline{\Lambda}$, and $\theta$ and $\eta$ are parameters. We investigate multiple solutions for this equation by using the variational methods. | ||
| کلیدواژهها | ||
| Kirchhoff type problem؛ Fourth-order operator؛ Variable exponent؛ Critical points؛ Variational methods | ||
| مراجع | ||
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[1] G.A. Afrouzi, M. Mirzapour, and N.T. Chung, Existence and multiplicity of solutions for Kirchhoff type problems involving p(x)-biharmonic operators, Z. Anal. Anwend. 33 (2014), no. 3, 289-303. [2] G.A. Afrouzi, M. Mirzapour, and N.T. Chung, Existence and non-existence of solutions for a p(x)-biharmonic problems, Electron. J. Differ. Equ. 2015 (2015), 1-8. [3] Z.E. Allali, M.K. Hamdani, and S. Taarabti, Three solutions to a Neumann boundary value problem driven by p(x)-biharmonic operator, J. Elliptic Parabol. Equ., 2024 (2024). [4] A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical points theory and applications, J. Funct. Anal. 14 (1973), 349-381. [5] A. Arosio and S. Panizzi, On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc. 348 (1996), 305-330. [6] M.M. Cavalcanti, V.N. Domingos Cavalcanti, and J.A. Soriano, Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation, Adv. Differ. Equ. 6 (2001), 701-730. [7] F.J.S.A. Correa and G.M. Figueiredo, On an elliptic equation of p-Kirchhoff type via variational methods, Bull. Aust. Math. Soc. 74 (2006), 263-277. [8] F.J.S.A. Correa and G.M. Figueiredo, On a p-Kirchhoff equation via Krasnoselskii's genus, Appl. Math. Lett. 22 (2009), 819-822. [9] G. Dai, R. Hao, Existence of solutions for a p(x)-Kirchhoff-type equation, J. Math. Anal. Appl. 359 (2009), 275-284. [10] G. Dai and R. Ma, Solutions for a p(x)-Kirchhoff-type equation with Neumann boundary data, Nonlinear Anal. 12 (2011), 2666-2680. [11] M. Dreher, The Kirchhoff equation for the p-Laplacian, Rend. Semin. Mat. Univ. Politec. Torino 64 (2006), 217-238. [12] M. Dreher, The wave equation for the p-Laplacian, Hokkaido Math. J. 36 (2007), 21-52. [13] A. El Amrouss, F. Moradi, and M. Moussaoui, Existence of solutions for fourth-order PDEs with variable exponentsns, Electron. J. Differ. Equ. 153 (2009), 1-13. [14] A. El Hamidi, Existence results to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl. 300 (2004), 30-42. [15] X.L. Fan and X. Fan, A Knobloch-type result for p(t)-Laplacian systems, J. Math. Anal. Appl. 282 (2003), 453-464. [16] X.L. Fan and X.Y. Han, Existence and multiplicity of solutions for -Laplacian equations in RN, Nonlinear Anal. T. M. A. 59 (2004), 173-188. [17] X.L. Fan and Q.H. Zhang, Existence of solutions for -Laplacian Dirichlet problems, Nonlinear Anal. T. M. A. 52 (2003), 1843-1852. [18] X.L. Fan and D. Zhao, On the spaces and , J. Math. Anal. Appl., 263 (2001), 424-446. [19] X.L. Fan, Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients, J. Math. Anal. Appl. 312 (2005), 464-477. [20] A. Ferrero and G. Warnault, On a solutions of second and fourth order elliptic with power type nonlinearities, Nonlinear Anal. T. M. A. 70 (2009), 2889-2902. [21] G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883. [22] L. Li and C.L. Tang, Existence and multiplicity of solutions for a class of -Biharmonic equations, Acta Math. Sci. 33 (2013), 155-170. [23] J.L. Lions, On some questions in boundary value problems of mathematical physics, Proc. Int. Symp. Continuum Mech. Partial Differ. Equ., Rio de Janeiro 1977, in: de la Penha, Medeiros (Eds.), Math. Stud., North-Holland 30 (1978), 284-346. [24] M. MihAilescu, Existence and multiplicity of solutions for a Neumann problem involving the -Laplace operator, Nonlinear Anal. T. M. A. 67 (2007), 1419-1425. [25] M. Ruzicka, Electrorheological fluids: modeling and mathematical theory, Lecture Notes in Mathematics 1748, Springer-Verlag, Berlin, 2000. [26] S. Taarabti, Z. El Allali, and K.B. Hadddouch, On the -Kirchhoff-type equation involving the -biharmonic operator via the genus theory, Ukr. Math. J., 72 (2020). [27] M. Willem, Minimax Theorems, Birkhauser, Boston, 1996. [28] Y. Wu, S. Taarabti, Z. El Allali, K. Ben Hadddouch, and J. Zuo, A class of fourth-order symmetrical Kirchhoff type systems, Symmetry 14 (2022). [29] J. Yao, Solutions for Neumann boundary value problems involving -Laplace operators, Nonlinear Anal. T. M. A. 68 (2008), 1271-1283. [30] A. Zang and Y. Fu, Interpolation inequalities for derivatives in variable exponent Lebesgue- Sobolev spaces, Nonlinear Anal. T. M. A. 69 (2008), 3629-3636. [31] J.F. Zhao, Structure Theory of Banach Spaces, Wuhan University Press, Wuhan, 1991. [In Chinese] [32] V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv. 9 (1987), 33-66. | ||
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