On the existence of solutions of boundary value problems for quasilinear elliptic equations of general form in Sobolev spaces
Kanat Tulenbayevkantulen05@outlook.comDepartment of Higher Mathematics and PhysicsAlmaty Technological UniversityAlmaty, 050012, Republic of KazakhstanView full profile → , *Gulnaz KarybayevaCorresponding authorkarybaygul@gmail.comDepartment of Higher Mathematics and PhysicsAlmaty Technological UniversityAlmaty, 050012, Republic of KazakhstanView full profile → , Assem ZhadyranovazhadAssem@outlook.comDepartment of Higher Mathematics and PhysicsAlmaty Technological UniversityAlmaty, 050012, Republic of KazakhstanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 17 Aug 2024
- Published Online:
- 19 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2182
- Pages:
- 1941–1954
Abstract
Keywords
Subject Classifications
References
[1] P. Gironimo, “Dirichlet problem for elliptic equations with coefficients in locally Morrey spaces,” Journal of Interdisciplinary Mathematics, vol. 23, no. 6, pp. 1109-1120 (2020). https://doi.org/10.1080/09720502.2020.1732050.
[2] A. Behzadan and M. Holst, “Multiplication in Sobolev spaces, revisited,” Arkiv för Matematik, vol. 59, no. 2, pp. 275-306 (2021).
[3] L. Brasco, D. Gómez-Castro and J. L. Vázquez, “Characterization of homogeneous fractional Sobolev spaces,” Calculus of Variations and Partial Differential Equations, vol. 60, no. 60 (2021).
[4] M. Borsuk, “Oblique derivative problem in a plane sector for strong quasi-linear elliptic second-order equation with perturbed p (x)-Laplacian,” Nonlinear Analysis, vol. 219, 112802 (2022).
[5] B. Emamizadeh, and Y. Liu, “Bang-bang and multiple valued optimal solutions of control problems related to quasi-linear elliptic equations,” SIAM Journal on Control and Optimization, vol. 58, no. 2, pp. 1103-1117 (2020).
[6] X. Dong and A. Mao, “Existence and multiplicity results for general quasilinear elliptic equations,” SIAM Journal on Mathematical Analysis, vol. 53, no. 4, pp. 4965-4984 (2021).
[7] Y. Jing, Z. Liu and Z. Q. Wang, “Parameter-dependent multiplicity results of sign-changing solutions for quasilinear elliptic equations,” Communications in Contemporary Mathematics, vol. 25, no. 9, pp. 1-8, 2250039 (2022).
[8] C. I. Cârstea and A. Feizmohammadi, “An inverse boundary value problem for certain anisotropic quasilinear elliptic equations,” Journal of Differential Equations, vol. 284, pp. 318-349 (2021).
[9] C. I. Argyros, I. K. Argyros, S. Regmi, J. A. John and J. Jayaraman, “Semi-local convergence of a seventh order method with one parameter for solving non-linear equations,” Foundations, vol. 2, no. 4, pp. 827-838 (2022).
[10] A. Tashimbetova, A. Rysbaeva, Z. Suleimenov, Z. Kalybekova and D. Sydykova, “Clusters in the gas dynamics and mathematical modeling in mathcade the results of the study,” International Journal of Engineering and Technology(UAE), vol. 7, no. 3.15 Special Issue 15, pp. 321-323 (2018). https://doi.org/10.14419/ijet.v7i2.29.13646.
[11] B. Y. Ashirbaev, “Solving the problem of analytical design of the controller for a stationary discrete system with a small step,” Journal of Physics: Conference Series, vol. 1864, no. 1, 012030 (2021). https://doi.org/10.1088/1742-6596/1864/1/012030.
[12] S. Kerimkhulle and Z. Aitkozha, “A criterion for correct solvability of a first order difference equation,” AIP Conference Proceedings, vol. 1880, 040016 (2017). https://doi.org/10.1063/1.5000632
[13] T. Al-Hawary, A. Amourah, J. Salah and F. Yousef, “Two Inclusive Subfamilies of bi-univalent Functions,” International Journal of Neutrosophic Science, vol. 24, no. 4, pp. 315-323 (2024). https://doi.org/10.54216/IJNS.240422
[14] A. Amourah, T. Al-Hawary, F. Yousef and J. Salah, “Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials,” International Journal of Neutrosophic Science, vol. 25, no. 1, pp. 228-238 (2025). https://doi.org/10.54216/IJNS.250121
[15] I. V. Kal’chuk, V. I. Kravets and U. Z. Hrabova, “Approximation of the classes WβrHα by three-harmonic Poisson integrals,” Journal of Mathematical Sciences (United States), vol. 246, no. 1, pp. 39-50 (2020). https://doi.org/10.1007/s10958-020-04721-4
[16] M. Lee and J. Ok, “Interior and boundary W1, q-estimates for quasi-linear elliptic equations of Schrödinger type,” Journal of Differential Equations, vol. 269, no. 5, pp. 4406-4439 (2020).
[17] S. S. Byun, N. Cho and H. S. Lee, “Maximal differentiability for a general class of quasilinear elliptic equations with right-hand side measures,” International Mathematics Research Notices, vol. 13, 9722-9754 (2022).
[18] A. A. Dmytruk, A. I. Gatalevych and M. I. Kuchma, “Stable range conditions for abelian and duo rings,” Matematychni Studii, vol. 57, no. 1, pp. 92-97 (2022). https://doi.org/10.30970/ms.57.1.92-97
[19] V. R. Zelisko and M.I. Kuchma, “Factorization of symmetric matrices over polynomial rings with involution,” Journal of Mathematical Sciences, vol. 96, no. 2, pp. 3017–3021. (1999). https://doi.org/10.1007/BF02169698
[20] V. Maz’ya, “Strong singularities of solutions to nonlinear elliptic equations,” in Mathematics Going Forward: Collected Mathematical Brushstrokes. Cham: Springer, 2022, pp. 499-503.
[21] A. Amourah, B. A. Frasin, J. Salah and T. Al-Hawary, “Fibonacci Numbers Related to Some Subclasses of Bi-Univalent Functions,” International Journal of Mathematics and Mathematical Sciences, vol. 2024, 8169496 (2024). https://doi.org/10.1155/2024/8169496
[22] J. Salah, H. U. Rehman, I. Al Buwaiqi, A. Al Azab and M. Al Hashmi, “Subclasses of spiral-like functions associated with the modified Caputo’s derivative operator,” AIMS Mathematics, vol. 8, no. 8, pp. 18474-18490 (2023). https://doi.org/10.3934/math.2023939
[23] N. Naceur, N. E. Alaa, M. Khenissi and J. R. Roche, “Theoretical and numerical analysis of a class of quasilinear elliptic equations,” Discrete & Continuous Dynamical Systems-Series S, vol. 14, no. 2, pp. 723-743 (2021).
[24] T. D. Do, L. X. Truong and N. N. Trong, “Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data,” Advanced Nonlinear Studies, vol. 21, no. 4, pp. 789-808 (2021).




