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Positive solutions for quasilinear system by using of weak sub-super solutions method and energy function | ||
| Caspian Journal of Mathematical Sciences | ||
| مقاله 12، دوره 13، شماره 1 - شماره پیاپی 25، 2024، صفحه 155-170 اصل مقاله (149.62 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2024.26868.1685 | ||
| نویسنده | ||
| Gholamreza Karamali* | ||
| Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran | ||
| تاریخ دریافت: 22 اسفند 1402، تاریخ بازنگری: 29 فروردین 1403، تاریخ پذیرش: 13 اردیبهشت 1403 | ||
| چکیده | ||
| In this paper we consider the quasilinear system \[ \left\{\begin{array}{ll} -\Delta_{p}u=\lambda g(x)f_{1}(u,v)+\mu h_{1}(u) ~~~~ in~~ x\in\Omega \\\\ -\Delta_{q}v=\lambda g(x)f_{2}(u,v)+\mu h_{2}(v) ~~~~ in~~ x\in \Omega \\\\ u(x)=v(x)=0 ~~~~ on ~~ x\in\partial\Omega~~. \end{array}\right. \] \\ where, $\Omega$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary $\partial\Omega,$ $\lambda>0$ is a parameter. Here $g$ is $C^1$ sign-changing function that may be negative near the boundary and $h_{1},h_{2},f_{1},f_{2}$ are nondecreasing and satisfy in additional conditions that we shall express the follow. Also we introduce the energy functional associate our problem then by energy functional we will discuss in context existence of solution for said problem. \end{abstract} | ||
| کلیدواژه‌ها | ||
| Positive solutions؛ quasilinear elliptic system؛ supersolution and subsolution؛ energy functional | ||
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آمار تعداد مشاهده مقاله: 52 تعداد دریافت فایل اصل مقاله: 78 |
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