Maximal domains of the $$(\lambda ,\mu )$$-parameters to existence of entire positive solutions for singular quasilinear elliptic systems

In this paper, we establish maximal domains on the real parameters $$\lambda ,\mu >0$$ to existence of $$C^{1}({\mathbb {R}}^{N})$$-entire positive solutions for the quasilinear elliptic system $$\begin{aligned} \left\{ \begin{array}{l} -\Delta _p u = \eta a(x)f_1(u) + \lambda b(x)g_1(u)h_1(v)~in ~ {\mathbb {R}}^N,\\ -\Delta _p v = \theta c(x)f_2(v) + \mu d(x)g_2(v)h_2(u)~in~ {\mathbb {R}}^N,\\ u, v > 0~in~ {\mathbb {R}}^N,~~ u(x), v(x) {\mathop {\longrightarrow }\limits ^{|x|\rightarrow \infty }} 0, \end{array} \right. \end{aligned}$$where $$\Delta _p$$ is the $$p-$$Laplacian operator with $$1< p< N $$ ($$3\le N$$); $$0

Keywords:

• Mathematics
• elliptic systems
• Lambda
• Mathematical analysis

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