Seminario di Analisi Matematica - Concentration and oscillation analysis of semilinear elliptic equations with exponential growth in a disc

Speaker: Daisuke Naimen (Muroran Institute of Technology)

We study infinite concentration and oscillation phenomena on semilinear elliptic equations with supercritical exponential growth in a disc. We first detect an infinite sequence of concentrating parts on blow-up solutions via the scaling technique. The precise description of each concentration is completed via the limit equation with suitable energy recurrence formulas. Thanks to this, we arrive at a key observation, the infinite concentration of blow-up solutions causes the infinite oscillation around singular solutions. This leads to a proof of infinite oscillations of bifurcation diagrams which yield the existence of infinitely many solutions.