Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions

Abstract

In this paper, we study positive one-dimensional solutions (i.e., solutions that depend only on one variable) for a class of semilinear elliptic problems in bounded cylinders in RN\mathbb R^N, N≥2N \geq 2. We compute the Morse index of such solutions and deduce from it the existence of least-energy solutions which are not one-dimensional, under suitable hypotheses on the nonlinearity and on the base of the cylinder. Furthermore, we analyze the appearance of more positive solutions, bifurcating from the one-dimensional ones, when we scale the base.Comment: 13 pages. Comments are welcom

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