Search results for "Fowler inversion"

Nodal Solutions for Supercritical Laplace Equations

2015

In this paper we study radial solutions for the following equation $$\Delta u(x)+f (u(x), |x|) = 0,$$ where $${x \in {\mathbb{R}^{n}}}$$ , n > 2, f is subcritical for r small and u large and supercritical for r large and u small, with respect to the Sobolev critical exponent $${2^{*} = \frac{2n}{n-2}}$$ . The solutions are classified and characterized by their asymptotic behaviour and nodal properties. In an appropriate super-linear setting, we give an asymptotic condition sufficient to guarantee the existence of at least one ground state with fast decay with exactly j zeroes for any j ≥ 0. Under the same assumptions, we also find uncountably many ground states with slow decay, singular gro…