Positive solutions of the p-Kirchhoff problem with degenerate and sign-changing nonlocal term

We establish the existence and multiplicity of positive solutions of the p -Kirchhoff problem - m ∫ Ω | ∇ u | p d x Δ p u = f ( u ) in Ω , u = 0 on ∂ Ω , where p > 1 , Ω is a smooth bounded domain of R N , and f ∈ C ( R 0 + ) ∩ L 1 ( R 0 + ) is subcritical and positive in a right neighborhood of...

Full description

Saved in:
Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2019-04, Vol.70 (2), p.1-12, Article 68
Main Authors: Le, Phuong, Huynh, Nhat Vy, Ho, Vu
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We establish the existence and multiplicity of positive solutions of the p -Kirchhoff problem - m ∫ Ω | ∇ u | p d x Δ p u = f ( u ) in Ω , u = 0 on ∂ Ω , where p > 1 , Ω is a smooth bounded domain of R N , and f ∈ C ( R 0 + ) ∩ L 1 ( R 0 + ) is subcritical and positive in a right neighborhood of zero. The main feature of our problem is that m : R 0 + → R may be any continuous function such that the integral of m in each connected component of m - 1 ( ( 0 , + ∞ ) ) is controlled by p , f and Ω . Therefore, in our paper m may be degenerate, i.e., it could vanish, and sign-changing at any number of different points.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-019-1114-2