Classification of the Solutions of Semilinear Elliptic Problems in a Ball
Benguria, Rafael; Dolbeault, Jean; Esteban, Maria J. (2000), Classification of the Solutions of Semilinear Elliptic Problems in a Ball, Journal of Differential Equations, 167, 2, p. 438-466. http://dx.doi.org/10.1006/jdeq.2000.3792
TypeArticle accepté pour publication ou publié
Journal nameJournal of Differential Equations
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Abstract (EN)In this paper we fully describe the set of the positive and nodal (regular and singular) radial solutions of the superlinear elliptic PDE. −Δu=λu+|u|p−1 u in B1, u=0 on ∂B1, p>1, (1)without restriction on the range of λset membership, variantImage . Here, B1 is the unit ball in Image 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.
Subjects / Keywordsnodal solutions; oscillatory solutions; multiplicity branches; bifurcations; critical exponent; Pohozaev's identity; semilinear elliptic equations; removable singularities
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