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Positive solutions for a class of quasilinear singular equations. (English) Zbl 1109.35309

The authors study the existence and uniqueness of solution of the problem \[ -\Delta_pu=\rho(x)\cdot f(u)\text{ in }\mathbb R^N,\quad u>0 \text{ in }\mathbb R^N, \lim_{|x|\to\infty}u(x)=0,\tag{1} \] where \(1<p< \infty\), \(N\geq 3\) and \(\Delta p\) is the \(p\)-Laplacian operators, while \(\rho:\mathbb R^N\to[0,\infty)\) is continuous and \(f:(0,\infty)\to(0,\infty)\) is a \(C^1\)-function, singular at zero. To this end, they use fixed-point arguments, the shooting method, and a lower-upper solutions argument.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
47N20 Applications of operator theory to differential and integral equations
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