پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 688 |
| تعداد مقالات | 9,994 |
| تعداد مشاهده مقاله | 70,986,062 |
| تعداد دریافت فایل اصل مقاله | 62,442,877 |
Positive solutions for multi-parameter cyclic $(p_1,\dots,p_n)$-Laplacian systems with combined and falling-zero nonlinearities | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 اسفند 1404 اصل مقاله (435.66 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.39875.5586 | ||
| نویسنده | ||
| Mahdi Choubin* | ||
| Department of Mathematics, Razi University, Kermanshah, Iran | ||
| تاریخ دریافت: 07 آذر 1404، تاریخ بازنگری: 02 دی 1404، تاریخ پذیرش: 10 دی 1404 | ||
| چکیده | ||
| We consider a cyclic $n\times n$ system of quasilinear elliptic equations \[ \begin{cases} - \Delta_{p_i} u_i = \lambda_i f_i(u_i) + \mu_i g_i(u_{i+1}), & i=1,2,\dots,n-1,\\%[1mm] - \Delta_{p_n} u_n = \lambda_n f_n(u_n) + \mu_n g_n(u_1), \end{cases} \] in a bounded smooth domain $\Omega\subset\mathbb{R}^N$ with homogeneous Dirichlet boundary conditions, where $\Delta_{p_i}z=\operatorname{div}(|\nabla z|^{p_i-2}\nabla z)$, $p_i>1$, and $\lambda_i,\mu_i>0$. The nonlinearities $f_i,g_i:[0,\infty)\to\mathbb{R}$ are increasing and satisfy a subcritical growth condition at infinity for $f_i$ and a combined sublinear composition condition for the cooperative chain $(g_i)_{i=1}^n$. This setting includes power-type and piecewise power-type nonlinearities. Under these assumptions, we prove the existence of positive weak solutions for all sufficiently large values of the sums $\lambda_i+\mu_i$. Under additional flatness conditions near the origin we obtain at least two distinct positive solutions. We also treat the case where $f_i$ have a falling-zero structure ($f_i>0$ on $(0,r_i)$, $f_i(r_i)=0$, $f_i<0$ on $(r_i,\infty)$) and derive analogous existence and multiplicity results. The proofs rely on the method of sub- and supersolutions and a three-solution theorem in an ordered Banach space. | ||
| کلیدواژهها | ||
| Multiple parameters؛ $(p_1؛ p_2؛ \dots؛ p_n)$-Laplacian systems؛ Combined sublinear effects؛ Falling zeroes؛ Sub- and supersolutions | ||
| مراجع | ||
|
[1] A. Abebe and M. Chhetri, A nonexistence result for p-Laplacian systems in a ball, Electron. J. Differ. Equ. 2023 (2023), no. Special Issue 2, 1–10.
[2] G.A. Afrouzi, S. Shakeri, and N.T. Chung, Remark on an infinite semipositone problem with indefinite weight and falling zeros, Proc. Indian Acad. Sci. (Math. Sci.) 123 (2013), 145–150.
[3] B. Alreshidi and D.D. Hai, An existence result for (p, q)-Laplacian BVP with falling zeros, Electron. J. Qual. Theory Differ. Equ. 2024 (32) (2024), 1–5.
[4] J. Ali and R. Shivaji, Positive solutions for a class of p-Laplacian systems with multiple parameters, J. Math. Anal. Appl. 335 (2007), 1013–1019.
[5] J. Ali, K. Brown, and R. Shivaji, Positive solutions for n×n elliptic systems with combined nonlinear effects, Differential Integral Equations 24 (3-4) (2011), 307-324.
[6] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620-709.
[7] A. Cañada, P. Drábek, and J.L. Gámez, Existence of positive solutions for some problems with nonlinear diffusion, Trans. Amer. Math. Soc. 349 (1997), 4231-4249.
[8] A. Cañada and J.L. Gámez, Some new applications of the method of lower and upper solutions to elliptic problems, Appl. Math. Lett. 6 (1993), 41-45.
[9] E.N. Dancer and G. Sweers, On the existence of a maximal weak solution for a semilinear elliptic equation, Differential Integral Equ. 2 (1989), 533-540.
[10] S. Khafagy and Z. Sadeghi, Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type, Eur. J. Math. Appl. 4 (2024), no. 11, 1-7.
[11] E.K. Lee, R. Shivaji, and J. Ye, Positive solutions for elliptic equations involving nonlinearities with falling zeros, Appl. Math. Lett. 22 (2009), 846-851.
[12] E.K. Lee, R. Shivaji, and J. Ye, Positive solutions for infinite semipositive problems with falling zeros, Nonlinear Anal. 72 (2010), 4475-4479.
[13] M. Nagumo, On principally linear elliptic differential equations of the second order, Osaka Math. J. 6 (1954), 207-229.
[14] E. Picard, Mémoire sur la théorie des équations aux dérivées partielles et la méthode des approximations successives, J. Math. Pures Appl. 6 (1890), 145-210.
[15] E. Picard, Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires, J. Math. Pures Appl. 9 (1893), 217-271.
[16] G. Scorza Dragoni, Il problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine, Giornale Mat. (Battaglini) 69 (1931), 77-112.
[17] R. Shivaji, A remark on the existence of three solutions via sub-super solutions, Nonlinear Anal. and Appl., CRC Press, 2020, pp. 561-566.
[18] S. Zeditri, K. Akrout, and R. Guefaïfa, Positive solution for a class of infinite semipositone (p,q)-Laplace system, Discont. Nonlinear. Complex. 11 (2022), no. 4, 757-765.
[19] A. Razani and G.M. Figueiredo, Degenerated and competing anisotropic (p,q)-Laplacians with weights, Appl. Anal. 102 (2023), no. 16, 4471-4488.
[20] A. Razani and G.M. Figueiredo, A positive solution for an anisotropic (p,q)-Laplacian, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 6, 1629-1643.
[21] D. Motreanu and A. Razani, Optimizing solutions with competing anisotropic (p,q)-Laplacian in hemivariational inequalities, Constr. Math. Anal. 7 (2024), no. 4, 150-159.
[22] A. Razani, A solution of a nonstandard Dirichlet Finsler (p,q)-Laplacian, Filomat 38 (2024), no. 23, 8131-8139.
[23] A. Razani, Nonstandard competing anisotropic (p,q)-Laplacians with convolution, Boundary Value Probl. 2022 (2022), Article 87.
[24] A. Razani and F. Safari, *Solutions to a (p1,...,pn)-Laplacian problem with Hardy potentials*, J. Nonlinear Math. Phys. 30 (2023), no. 2, 413-427.
[25] A. Razani and S. Baraket, Non-variational solutions for anisotropic (p,q)-Laplacian systems with nonhomogeneous growth, Bull. Iran. Math. Soc. 51 (2025), Article 83.
[26] M. Mahshid and A. Razani, *Infinitely many solutions for a class of systems including the (p1,...,pn)-biharmonic operators*, Filomat 36 (2022), no. 7, 2303-2310.
| ||
|
آمار تعداد مشاهده مقاله: 1 تعداد دریافت فایل اصل مقاله: 2 |
||