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}
Karamali, G. (2024). Positive solutions for quasilinear system by using of weak sub-super solutions method and energy function. Caspian Journal of Mathematical Sciences, 13(1), 155-170. doi: 10.22080/cjms.2024.26868.1685
MLA
Gholamreza Karamali. "Positive solutions for quasilinear system by using of weak sub-super solutions method and energy function", Caspian Journal of Mathematical Sciences, 13, 1, 2024, 155-170. doi: 10.22080/cjms.2024.26868.1685
HARVARD
Karamali, G. (2024). 'Positive solutions for quasilinear system by using of weak sub-super solutions method and energy function', Caspian Journal of Mathematical Sciences, 13(1), pp. 155-170. doi: 10.22080/cjms.2024.26868.1685
VANCOUVER
Karamali, G. Positive solutions for quasilinear system by using of weak sub-super solutions method and energy function. Caspian Journal of Mathematical Sciences, 2024; 13(1): 155-170. doi: 10.22080/cjms.2024.26868.1685
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