Positive Solutions for an Iterative System of Nonlinear Elliptic Equations
Tóm tắt
This paper deals with the existence of positive radial solutions to the iterative system of nonlinear elliptic equations of the form
$$\begin{aligned} \begin{aligned} \triangle {\mathtt {z}_{\mathtt {j}}}+\frac{(\mathtt {N}-2)^2r_0^{2\mathtt {N}-2}}{\vert x\vert ^{2\mathtt {N}-2}}\mathtt {z}_\mathtt {j}+\varphi (\vert x\vert )\mathtt {g}_{\mathtt {j}}(\mathtt {z}_{\mathtt {j}+1})=0,~\mathtt {R}_1<\vert x\vert <\mathtt {R}_2, \end{aligned} \end{aligned}$$
where
$$\mathtt {j}\in \{1,2,3,\cdot \cdot \cdot ,\ell \},$$
$$ \mathtt {z}_1= \mathtt {z}_{\ell +1},$$
$$\triangle {\mathtt {z}}=\mathtt {div}(\triangledown \mathtt {z}),$$
$$\mathtt {N}>2,$$
$$0
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