دانشگاه سمنان

 آمار

تعداد نشریات22
تعداد شماره‌ها705
تعداد مقالات10,146
تعداد مشاهده مقاله71,449,582
تعداد دریافت فایل اصل مقاله63,173,681
Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. (1401). Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators. هنرهای کاربردی, 14(1), 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Yacini Soukaina; Mohamed El Ouaarabi; Allalou Chakir; Hilal Khalid. "Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators". هنرهای کاربردی, 14, 1, 1401, 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. (1401). 'Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators', هنرهای کاربردی, 14(1), pp. 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014
Soukaina, Yacini, El Ouaarabi, Mohamed, Chakir, Allalou, Khalid, Hilal. Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators. هنرهای کاربردی, 1401; 14(1): 3201-3210. doi: 10.22075/ijnaa.2023.28884.4014

Existence result for double phase problem involving the $(p(x),q(x))$-Laplacian-like operators

International Journal of Nonlinear Analysis and Applications
مقاله 250، دوره 14، شماره 1، فروردین 2023، صفحه 3201-3210    اصل مقاله (405.74 K)
نوع مقاله: Review articles
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28884.4014
نویسندگان
Yacini Soukaina* 1؛ Mohamed El Ouaarabi2؛ Allalou Chakir2؛ Hilal Khalid2
1Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
2Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
تاریخ دریافت: 12 آبان 1401،  تاریخ بازنگری: 18 دی 1401،  تاریخ پذیرش: 23 دی 1401 
چکیده
The paper study the existence of at least one weak solutions for Dirichlet boundary value problem involving the $\big(p(x),q(x)\big)$-Laplacian-like operators of the following form:
\begin{equation*}
\displaystyle\left\{\begin{array}{ll}
\displaystyle-\Delta^{l}_{p(x)}-\Delta^{l}_{q(x)}=\lambda g(x, u, \nabla u) & \mathrm{i}\mathrm{n}\ \Omega,\\\\
u=0 & \mathrm{o}\mathrm{n}\ \partial\Omega,
\end{array}\right.
\end{equation*}
where $\Delta^{l}_{r(x)} $ is the $r(x)$-Laplacian-like operators, $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$, $\lambda$ is a real parameter and $g$ is Carath'eodory function satisfies the assumption of growth. The existence is proved by using Berkovits' topological degree.
کلیدواژه‌ها
Dirichlet problems؛ double phase problems؛ (p(x),q(x))- Laplacian-like operators؛ topological degree methods
مراجع

[1] A. Abbassi, C. Allalou and A. Kassidi, Existence results for some nonlinear elliptic equations via topological degree methods, J. Elliptic Parabol Equ. 7 (2021), 121–136.

[2] A. Aberqi, O. Benslimane, M. Elmassoudi and M.A. Ragusa, Nonnegative solution of a class of double phase problems with logarithmic nonlinearity, Boundary Value Prob. 2022 (2022), no. 1, 1–57.

[3] E. Acerbi and G. Mingione, Regularity results for a class of functionals with nonstandard growth, Arch. Ration. Mech. Anal. 156 (2001), 121–140.

[4] C. Allalou and K. Hilal, Weak solution to p (x)-Kirchoff type problems under no-flux boundary condition by topological degree, Bol. Soc. Paranaense Mat. 41 (2023), 1–12.

[5] J. Berkovits, Extension of the Leray-Schauder degree for abstract Hammerstein type mappings, J. Differ. Equ. 234 (2007), 289–310.

[6] F. Behboudi and A. Razani, Two weak solutions for a singular (p, q)-Laplacian problem, Filomat 33 (2019), no. 11, 3399–3407.

[7] X.L. Fan and D. Zhao, On the spaces L p(x) (Ω) and W m,p(x) (Ω), J. Math. Anal. Appl. 263 (2001), 424–446.

[8] P. Harjulehto, P. Hasto, M. Koskenoja and S. Varonen, The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal. 25 (2006), 205–222.

[9] S. Heidari and A. Razani, Iinfinitely many solutions for (p (x), q (x))-Laplacian-Like systems, Commun. Korean Math. Soc. 36 (2021), no. 1, 51–62.

[10] I.H. Kim and Y.H. Kim, Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents, Manuscripta Math. 147 (2015), no. 1-2, 169–191.

[11] I.S. Kim and S.J. Hong, A topological degree for operators of generalized (S+) type, Fixed Point Theory Appl. 2015 (2015), no. 1, 1–16.

[12] O. Kovacik and J. Rakosnık, On spaces Lp(x) and W1,p(x) , Czech. Math. J. 41 (1991), no. 4, 592–618.

[13] M. Mahshi and A. Razani, A weak solution for a (p(x), q(x))-Laplacian elliptic problem with a singular term, Boundary Value Prob. 2021 (2021), 80.

[14] W.M. Ni and J. Serrin, Non-existence theorems for quasilinear partial differential equations, Rend. Circ. Mat. Palermo (2) Suppl. 8 (1985), 171–185.

[15] W.M. Ni and J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Att. Conveg. Lincei. 77 (1986), 231–257.

[16] M.E. Ouaarabi, A. Abbassi and C. Allalou, Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces, J Elliptic Parabol Equ. 7 (2021), no. 1, 221–242.

[17] M.E. Ouaarabi, A. Abbassi and C. Allalou, On the Dirichlet problem for some nonlinear degenerated elliptic equations with weight, 7th Int. Conf. Optim. Appl., 2021, pp. 1–6.

[18] M.E. Ouaarabi, A. Abbassi and C. Allalou, Existence result for a general nonlinear degenerate elliptic problems with measure datum in weighted Sobolev spaces, Int. J. Optim. Appl. 1 (2021), no. 2, 1–9.

[19] K.R. Rajagopal and M. R ˙uzicka, Mathematical modeling of electrorheological materials, Contin. Mech. Thermodyn. 13 (2001), no. 1, 59–78.

[20] M.A. Ragusa, A. Razani and F. Safari, Existence of radial solutions for a p(x)-Laplacian Dirichlet problem, Adv. Differ. Equ. 2021 (2021), 215.

[21] A. Razani, Two weak solutions for fully nonlinear Kirchhoff-type problem, Filomat 35 (2021), no. 10, 3267–3278.

[22] M. Manuela Rodrigues, Multiplicity of solutions on a nonlinear eigenvalue problem for p(x)-Laplacian-like operators, Mediterr J Math. 9 (2012), 211–223.

[23] M. Ruzicka, Electrorheological fuids: Modeling and mathematical theory, Lecture Notes in Mathematics, Berlin Springer Verlag, 2000.

[24] S.G. Samko, Density of C∞ 0 (R N ) in the generalized Sobolev spaces W m,p(x) (R N ), Doklady Math. 60 (1999), no. 3, 382–385.

[25] S. Shokooh and A.Neirameh, Existence results of infinitely many weak solutions for p(x)-Laplacian-like operators, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 78 (2016), no. 4, 95–104.

[26] C. Vetro, Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), no. 98, 1–10.

[27] S. Yacini, C. Allalou, K. Hilal and A.Kassidi, Weak solutions to Kirchhoff type problems via topological degree, Adv. Math. Mod. Appl. 6 (2021), no. 3, 309–321.

[28] E. Zeidler, Nonlinear functional analysis and its applications, II/B: Nonlinear monotone operators, Springer-Verlag, New York, 1990.

[29] Q.M. Zhou, On the superlinear problems involving p(x)-Laplacian-like operators without AR-condition. Nonlinear Anal. Real World Appl. 21 (2015), 161–169.

آمار
تعداد مشاهده مقاله: 17,709
تعداد دریافت فایل اصل مقاله: 12,633


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب