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- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제36권 제3호
- 발행연도
- 2018.1
- 수록면
- 173 - 179 (7page)
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In this paper, we investigate the stability of positive weak solution for the singular p-Laplacian nonlinear system $-div[{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u]+m(x){\mid}u{\mid}^{p-2}u={\lambda}{\mid}x{\mid}^{-(a+1)p+c}b(x)f(u)$ in ${\Omega}$, Bu = 0 on ${\partial}{\Omega}$, where ${\Omega}{\subset}R^n$ is a bounded domain with smooth boundary $Bu={\delta}h(x)u+(1-{\delta})\frac{{\partial}u}{{\partial}n}$ where ${\delta}{\in}[0,1]$, $h:{\partial}{\Omega}{\rightarrow}R^+$ with h = 1 when ${\delta}=1$, $0{\in}{\Omega}$, 1 < p < n, 0 ${\leq}$ a < ${\frac{n-p}{p}}$, m(x) is a weight function, the continuous function $b(x):{\Omega}{\rightarrow}R$ satisfies either b(x) > 0 or b(x) < 0 for all $x{\in}{\Omega}$, ${\lambda}$ is a positive parameter and $f:[0,{\infty}){\rightarrow}R$ is a continuous function. We provide a simple proof to establish that every positive solution is unstable under certain conditions.
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참고문헌 (19)
참고문헌 신청
G. Afrouzi / 2006 / Stability properties of non-negative solutions to a non-autonomous p-Laplacian equation / Chaos, Solitons and fractals 29:1095~1099
G. Afrouzi / 2008 / On the stability of nonnegative solutions to classes of p-Laplacian systems / World Journal of modelling and Simulation 4:149~152
G. Afrouzi / 2008 / Stability results for a class of elliptic problems / International Journal of Nonlinear Science 6:114~117
I. Ali / 1993 / Uniqueness and stability of nonnegative solutions for semipositone problems in a ball / Proc. Amer. Math. Soc 117:775~782
C. Atkinson / 1992 / Some boundary value problems for the Bingham model / J. Non-Newton. Fluid Mech. 41:339~363
G. Afrouzi / 2008 / On the stability of nonnegative solutions to classes of p-Laplacian systems / World Journal of modelling and Simulation 4:149~152
G. Afrouzi / 2008 / Stability results for a class of elliptic problems / International Journal of Nonlinear Science 6:114~117
I. Ali / 1993 / Uniqueness and stability of nonnegative solutions for semipositone problems in a ball / Proc. Amer. Math. Soc 117:775~782
C. Atkinson / 1992 / Some boundary value problems for the Bingham model / J. Non-Newton. Fluid Mech. 41:339~363
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