
تعداد نشریات | 21 |
تعداد شمارهها | 622 |
تعداد مقالات | 9,157 |
تعداد مشاهده مقاله | 67,490,085 |
تعداد دریافت فایل اصل مقاله | 8,019,159 |
On a class of Schrodinger-Kirchhoff-Poisson systems | ||
International Journal of Nonlinear Analysis and Applications | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 16 فروردین 1404 اصل مقاله (406.81 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.35087.5241 | ||
نویسندگان | ||
Meysam Soluki* 1؛ Ghasem Alizadeh Afrouzi1؛ Seyed Hashem Rasouli2 | ||
1Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran | ||
2Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Babol, Iran | ||
تاریخ دریافت: 24 مرداد 1403، تاریخ پذیرش: 28 شهریور 1403 | ||
چکیده | ||
This article discusses the existence and multiplicity of solutions for the following Schrodinger-Kirchhoff-Poisson system: \begin{equation*} \left\{\begin{array}{ll} \displaystyle -(a+b\int_{\mathbb{R}^3} |\nabla u|^2)\Delta u + \lambda \phi u=m(x){|u|}^ {q-2} u+ f(x,u), \qquad x \in \Omega,\\ \displaystyle\\ \displaystyle -\Delta\phi=u^2,~~\qquad\qquad\qquad ~\qquad x \in \Omega, \end{array}\right. \end{equation*} where $\Omega$ is a bounded smooth domain of $\mathbb{R}^3$, $a\geq 0$ ,$b> 0$ and $\lambda > 0$ is a parameter, $ 1<q<2$ and $f(x,u)$ is linearly bounded in $u$ at infinity. Under some suitable assumptions on $m$ and $f$, we prove the existence and multiplicity of solutions via variational methods. | ||
کلیدواژهها | ||
Schrodinger-Kirchhoff-Poisson systems؛ Combined nonlinearity؛ Variational methods | ||
مراجع | ||
[1] C.O. Alves and M.A.S. Souto, Existence of least energy nodal solution for a Schrodinger- Poisson system in bounded domains, Z. Angew. Math. Phys. 65 (2014), 1153–1166. [2] C.O. Alves and G.M. Figueiredo, Existence of positive solution for a planar Schrodinger-Poisson system with exponential growth, J. Math. Phys. 60 (2019), no. 1. [3] G. Anelo, A uniqueness result for a nonlocal equation of Kirchhoff equation type and some related open problem, J. Math. Anal. Appl. 373 (2011), 248–251. [4] G. Anelo, On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type, Bound. Value Prob. 2011 (2011), 1-10. [5] A. Ambrosetti and D. Ruiz, Multiple bound states for the Schrodinger-Poisson problem, Contemp. Math. 10 (2008), 391–404. [6] A. Azzollini and A. Pomponio, Ground state solutions for the nonlinear Schrodinger-Maxwell equations, J. Math. Anal. Appl. 345 (2008), 90–108. [7] C.J. Batkam, Multiple sign-changing solutions to a class of Kirchhoff type problems, Electronic J. Differ. Equ. 2016 (2016). [8] C.J. Batkam and J.R.S. Junior, Schrodinger-Kirchhoff-Poisson type systems, Commun. Pure Appl. Anal. 15 (2016), 429–444. [9] V. Benci and D. Fortunato, An eigenvalue problem for the Schrodinger-Maxwell equations, Meth. Nonlinear Anal. 11 (1998), 283–293. [10] G. Cerami and G. Vaira, Positive solutions for some non-autonomous Schrodinger-Poisson systems, J. Differ. Equ. 248 (2010), 521–543. [11] G.M. Coclite, A multiplicity result for the nonlinear Schrodinger-Maxwell equations, Commun. Appl. Anal. 7 (2003), 417–423. [12] L. Cui and A. Mao, Existence and asymptotic behavior of positive solutions to some logarithmic Schrodinger–Poisson system, Z. Angew. Math. Phys. 75 (2024), no. 1, 30. [13] T. D’Aprile and D. Mugnai, Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrodinger-Maxwell equa[1]tions, Proc. Roy. Soc. Edinburgh. Sect. A 134 (2004), 893–906. [14] X. Feng, H. Liu, and Z. Zhang, Normalized solutions for Kirchhoff type equations with combined nonlinearities: The Sobolev critical case, Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 2935–2972. [15] G.M. Figueiredo, N. Ikoma, and J.R. Santos Junior, Existence and concentration result for the Kirchhoff type equations with general nonlinearities, Arch. Ration. Mech. Anal. 213 (2014), 931–979. [16] G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883. [17] D. Ruiz, The Schrodinger-Poisson equation under the effect of a nonlinear local term, J. Funct. Anal. 237 (2006), 655–674. [18] D. Ruiz and G. Siciliano, A note on the Schrodinger-Poisson-Slater equation on bounded domains, Adv. Nonlinear Stud. 8 (2008), 179–190. [19] M. Soluki, G.A. Afrouzi, and S.H. Rasouli, Existence and multiplicity of non-trivial solutions for fractional Schr¨odinger-Poisson systems with a combined nonlinearity, J. Ellip. Parab. Equ. 10 (2024), 211-224. [20] M. Soluki, S.H. Rasouli, and G.A. Afrouzi, On a class of nonlinear fractional Schrodinger-Poisson systems, Int. J. Nonlinear Anal. Appl. 10 (2019), 123–132. [21] M. Soluki, S.H. Rasouli, and G.A. Afrouzi, Solutions of a Schr¨odinger-Kirchhoff-Poisson system with concave-convex nonlinearities, J. Ellip. Parab. Equ. 9 (2023), no. 2, 1233–1244. [22] M. Soluki, G.A. Afrouzi, and S.H. Rasouli, Existence of non-trivial solutions to a class of fractional p-Laplacian equations of Schrodinger-type with a combined nonlinearity, J. Anal. 32 (2024), no. 5, 2847–2856. [23] L. Shao and H. Chen, Existence of solutions for the Schrodinger-Kirchhoff-Poisson systems with a critical non[1]linearity, Bound. Value Prob. 210 (2016), 1–11. [24] M. Sun, J. Su, and L. Zhao, Solutions of a Schrodinger-Poisson system with combined nonlinearities, J. Math. Anal. Appl. 442 (2016), 385–403. [25] Z. Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, Nonlinear Differ. Equ. Appl. 8 (2001), 15–33. [26] F. Zhao and L. Zhao, Positive solutions for Schrodinger-Poisson equations with a critical exponent, Nonlinear Anal. 70 (2009), 2150–2164. [27] J. Zhang, H. Liu, and J. Zuo, High energy solutions of general Kirchhoff type equations without the Ambrosetti-Rabinowitz type condition, Adv. Nonlinear Anal. 12 (2023), no. 1. | ||
آمار تعداد مشاهده مقاله: 25 تعداد دریافت فایل اصل مقاله: 28 |