Positive solutions for a Kirchhoff problem with vanishing nonlocal term

By Joao R. Santos J'unior, Gaetano Siciliano. Journal of Differential Equations, 2018

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Abstract In this paper we study the Kirchhoff problem { − m ( ‖ u ‖ 2 ) Δ u = f ( u ) in  Ω , u = 0 on  ∂ Ω , in a bounded domain, allowing the function m to vanish in many different points. Under an appropriated 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 H 0 1 ( Ω ) -norm.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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