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Localized radial solutions for a nonlinear \(p\)-Laplacian equation in \(\mathbb{R}^N\). (English) Zbl 1183.34040

Summary: We establish the existence of radial solutions to the \(p\)-Laplacian equation
\[ \Delta_p u + f(u)=0 \] in \(\mathbb {R^N}\), where \(f\) behaves like \(|u|^{q-1}u\) when \(u\) is large and \(f(u) < 0\) for small positive \(u\). We show that for each nonnegative integer \(n\), there is a localized solution \(u\) which has exactly \(n\) zeros.

MSC:

34B40 Boundary value problems on infinite intervals for ordinary differential equations
35J60 Nonlinear elliptic equations
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