2025/05/13 by Precup, Radu, Stan, Andrei · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.08678
In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of Krasnoselskii's compression-extension theorem or topological index methods, our approach uses the Nehari manifold technique in a surprising combination with the cone version of Birkhoff-Kellogg's invariant-direction theorem. This yields a simpler alternative to traditional methods involving deformation arguments or Ekeland variational principle. The new method is illustrated on a boundary value problem for p-Laplacian equations, and we believe that it will be useful for proving the existence, localization, and multiplicity of solutions for other classes of problems with variational structure.