Classification of the solutions of semilinear elliptic problems in a ball

[摘要] In this paper we fully describe the set of the positive and nodal (regular and singular) radial solutions of the superlinear elliptic PDE. = Deltau = lambdau + (u)(p-1) u in B-1. u = 0 on partial derivativeB(1). p >1. (1) without restriction on the range of lambda is an element of R. Here, B-1 is the unit ball in R-N. More precisely, in all subcritical, critical and supercritical cases, we analyze the possible singularities of radial solutions at the origin and the number of bounded and unbounded solutions. The solutions will be of three different types: bounded with a finite number of zeroes in (0, 1), singular at the origin, still with a finite number of zeroes and singular with sign changing oscillations at the origin. (C) 2000 Academic Press.

[发布日期] 2000-11-01

[关键词] nodal solutions;oscillatory solutions;multiplicity branches;bifurcations;critical exponent;Pohozaev's identity;semilinear elliptic equations;removable singularities