Journal of Nonlinear Sciences and Applications(JNSA)Journal of Nonlinear Sciences and ApplicationsJNSA 2008-1898 2008-1901International Scientific Research PublicationsJohor, Malaysiainfo@isr-publications.comisr-publications.comisr-publications.com/jnsa10.22436/jnsa.001.02.01SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMSALIMOHAMMADY M.
Islamic Azad University, branch Noor, Iran
KOOZEGARM.
Department of Mathematics, University of Mazandaran, Babolsar 47416 - 1468, Iran.
This paper deals with nonexistence result for positive solution in $$C^1(\overline{\Omega})$$ to the following reaction-diffusion system $\begin{cases} -\Delta_{a,p}u = a_1v^{p-1} - b_1v^{\gamma -1} - c,\,\,& \,\,x\in \Omega,\\ -\Delta_{a,p}v = a_1u^{p-1} - b_1u^{\gamma -1} - c,\,\,& \,\,x\in \Omega, \qquad (0.1)\\ u = 0 = v \,\,& \,\,x\in \partial \Omega, \end{cases}$ where $$\Delta_{a,p}$$ denotes the $$a, p$$-Laplacian operator defined by $$\Delta_{a,p}z=div(a| \nabla z|^{p-2}\nabla z); p>1, \gamma(>p); a_1, b_1$$ and $$c$$ are positive constant, $$\Omega$$­ is a smooth bounded domain in $$\mathbb{R}^N(N \geq1)$$ with smooth boundary and $$a(x) \in L^\infty(\Omega­), a(x) \geq a_0 > 0$$ for all $$x\in\Omega$$ ­.