Positive solutions for Kirchhoff problems with vanishing nonlocal term

2017/09/19 by Júnior, João R. Santos, Siciliano, Gaetano
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.06463

Abstract

In this paper we study the Kirchhoff problem \ -m(‖ u ‖²)Δu = f(u) · amp; in Ω, u=0 · amp; on ∂Ω,. in a bounded domain, allowing the function m to vanish in many different points. Under an appropriated \sl area condition, by using a priori estimates, truncation techniques and variational methods, we prove a multiplicity result of positive solutions which are ordered in the H₀¹(Ω)-norm.

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