GLOBAL BIFURCATION AND LOCAL MULTIPLICITY RESULTS FOR ELLIPTIC EQUATIONS WITH SINGULAR NONLINEARITY OF SUPER EXPONENTIAL GROWTH IN ?~2

摘要

In this paper, we study the solutions to the following singular elliptic problem of exponential type growth posed in a bounded smooth domain ? ? ?~2: Here, 1 ≤ α ≤ 2, 0 < δ < 3, λ ≥ 0 and h(t) is assumed to be a smooth "perturbation" of e~t~α as t → ∞ (see (H1) - (H2) below). We show the existence of an unbounded connected branch of solutions to (P_λ) emanating from the trivial solution at λ = 0. In the radial case (i. e., when Ω = B_1 and u is radially symmetric) we make a detailed study of the blow-up/convergence of the solution branch as it approaches the asymptotic bifurcation point at infinity. In the critical case a = 2, we interpret the multiplicity results in terms of the corresponding bifurcation diagrams and the asymptotic profile of large solutions along the branch at infinity.