Semi linear elliptic system at resonance

	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
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
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