Convergence for radially symmetric solutions of quasilinear elliptic equations is generic (Q1392402)

Consider the semilinear equation \[ \Delta w+ f(w)= 0.\tag{1} \] The radial part \(u= u(t)\) of a radially symmetric solution \(w(x)\), \(t= | x|\) to (1) is called a solution to the singular initial value problem \[ u''+ [(n- 1)/t]u'+ f(u)= 0\quad (t>0),\quad u(0)= p,\quad u'(0)= 0,\tag{2} \] with \(w(0)= p\). It was proved previously that for any \(f\in C^1(\mathbb{R})\) which has a regular value \(0\) the solutions to (2) are convergent. Hence it may be deduced that any nonconvergent solution to (2) is bounded and has an infinite number of isolated critical points. Here, the author proves many results in this direction concerning radially symmetric solutions to quasilinear elliptic equations.