On critical exponent for the existence and stability properties of positive weak solutions for some nonlinear elliptic systems involving the (<Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">q</Emphasis>)-Laplacian and indefinite weight function

This paper deals with the existence and stability properties of positive weak solutions to classes of nonlinear systems involving the (p,q)-Laplacian of the form

$ \left\{{ll} -\Delta_{p} u = \lambda \,a(x)\,v^{\alpha}-c, & x\in \Omega,\\ -\Delta_{q} v = \lambda \,b(x)\,u^{\beta}-c, & x\in \Omega,\\ u=0=v, & x\in\partial \Omega, \right. $ \left\{\begin{array}{ll} -\Delta_{p} u = \lambda \,a(x)\,v^{\alpha}-c, & x\in \Omega,\\ -\Delta_{q} v = \lambda \,b(x)\,u^{\beta}-c, & x\in \Omega,\\ u=0=v, & x\in\partial \Omega, \end{array}\right.
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