Kirchhoff-type problems involving subcritical and superlinear nonlinearities satisfying no further condition

2017/10/16 by Biagio Ricceri, Ricceri, Biagio
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1710.05676

openalex publication_date 2017/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we deal with a problem of the type \cases -h ( ∫_Ω|∇ u(x)|²dx ) Δu=f(u) amp; in Ω\cr amp; \cr u_|∂Ω=0 .\cr As an application of a new general multiplicity result, we establish the existence of at least three solutions, two of which are global minima of the related energy functional. The only condition assumed on f is that it be subcritical and superlinear: no condition on the behaviour of f at 0 is requested.

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