# SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS

Volume 1, Issue 2, pp 56-60
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### Authors

M. ALIMOHAMMADY - Islamic Azad University, branch Noor, Iran. M. KOOZEGAR - Department of Mathematics, University of Mazandaran, Babolsar 47416 - 1468, Iran..

### Abstract

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 $x\in\Omega$ ­.

### Share and Cite

##### ISRP Style

M. ALIMOHAMMADY, M. KOOZEGAR, SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 2, 56-60

##### AMA Style

ALIMOHAMMADY M., KOOZEGAR M., SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS. J. Nonlinear Sci. Appl. (2008); 1(2):56-60

##### Chicago/Turabian Style

ALIMOHAMMADY , M., KOOZEGAR, M.. "SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME alpha, P-LAPLACIAN SYSTEMS." Journal of Nonlinear Sciences and Applications, 1, no. 2 (2008): 56-60

### Keywords

• p
• a-Laplacian
• nonexistence
• positive solution
• reaction-diffusion systems.

•  35P20
•  35J70
•  35BJ20

### References

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