Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 15, pp. 1-14.
Title: Multiple positive solutions for quasilinear elliptic systems
Authors: Qin Li (Nanjing Normal Univ., China)
Zuodong Yang (Nanjing Normal Univ., China)
Abstract:
In this article, we investigate how the coefficient $f(z)$ affects
the number of positive solutions of the quasilinear elliptic system
$$\displaylines{
-\Delta_{p}u =\lambda g(z)|u|^{q-2}u+\frac{\alpha}{\alpha+\beta}
f(z)|u|^{\alpha-2}u|v|^{\beta} \quad\hbox{in }\Omega,\cr
-\Delta_{p}v =\mu h(z)|v|^{q-2}v
+\frac{\beta}{\alpha+\beta}f(z)|u|^{\alpha}|v|^{\beta-2}v
\quad\hbox{in }\Omega,\cr
u=v=0\quad\hbox{on }\partial\Omega,
}$$
where $0\in\Omega\subset \mathbb{R}^{N}$ is a bounded domain,
$\alpha >1$, $\beta>1$ and $12p$.
Submitted July 6, 2012. Published January 17, 2013.
Math Subject Classifications: 35J65, 35J50.
Key Words: Quasilinear elliptic systems; multiple positive solutions;
critical point, Nehari manifold.