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Semi linear elliptic system at resonance | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 15، شماره 2، اردیبهشت 2024، صفحه 369-377 اصل مقاله (354.58 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31401.4625 | ||
| نویسنده | ||
| Ouahiba Gharbi* | ||
| Departement of Mathematics, Faculty of Science; Badji Mokhtar University, Annaba, Algeria | ||
| تاریخ دریافت: 10 تیر 1402، تاریخ بازنگری: 23 مرداد 1402، تاریخ پذیرش: 24 مرداد 1402 | ||
| چکیده | ||
| In this work, we investigate the existence of weak solutions for the following semi-linear elliptic system \begin{equation*} \left\{ \begin{array}{c} -\Delta u+p(x)u=\alpha u+\phi \left( x,v\right) \ \ \ \ \text{in }\Omega , \\ -\Delta v+q(x)v=\beta v+\psi \left( x,u\right) \ \ \ \ \text{in }\Omega ,% \end{array} \right. \end{equation*} with Dirichlet boundary condition, where $\Omega $ is a bounded open set of $\mathbb{R}^{N}$ $\left( N\geq 2\right) ,$ $\alpha ,\beta $ two real parameters, $\left( p(x),q(x)\right) \in \left( L^{\infty }\left( \Omega \right) \right) ^{2}$ and $p(x),q(x)\geq 0.$ using the Leray-Schauder's topological degree and under some suitable conditions for the non linearities $\phi $ and $\psi$, we show the existence of nontrivial solutions. | ||
| کلیدواژه‌ها | ||
| Homotopy؛ Boundary value problem؛ Fixed point theorems | ||
| مراجع | ||
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[1] T. Gallouet and O. Kavian, Resultats d’existence et de non-existence pour certains problemes demi-lineaires a l’infini, Ann. Fac. Sci. Toulouse 3 (1981), no. 3-4, 201–246. [2] S. Heidari, A. Razani, Infinitely many solutions for (p(x), q(x))-Laplacian-like systems, Commun. Korean Math. Soc. 36 (2021), no. 1, 51–62 [3] A. Khaleghi and A. Razani, Solutions to a (p(x), q(x))-biharmonic elliptic problem on a bounded domain, Bound. Value Prob. 2023 (2023), Article number: 53. [4] M.A. Ragusa, A. Razani, and F. Safari, Existence of radial solutions for a p(x)-Laplacian Dirichlet problem, Adv. Differ. Equ. 2021 (2021), Article number: 215. [5] A. Razani and G.M. Figueiredo, Weak Solution by the Sub-Super solution method for a nonlocal system involving Lebrsgue generalized spaces, Electronic J. Differ. Equ. 2022 (2022), no. 36, 1–18. | ||
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