The \(p\)-Laplacian equation with superlinear and supercritical growth, multiplicity of radial solutions (Q1763866)

The Dirichlet problem for the \(p\)-Laplacian equation is considered. The nonlinearity contains superlinear and supercritical growth. Existence, multiplicity, and asymptotic behaviour is studied for radially symmetric solutions. The considered problem is transformed to the form \[ p^{1-n}(r^{n-1}| u_r'|^{p-2}u_r')'+f(u)=0, \] \[ u_r'(0)=0,\quad u(R)=0, \] where \(f(u)=u^\gamma+u^\delta\) for \(u\geq 0\), and \(f(u)=0\) otherwise.