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

Authors: 

Phuong Le, Nhat Vy Huynh and Vu Ho

Source title: 
Zeitschrift Fur Angewandte Mathematik Und Physik, 70:68, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

We establish the existence and multiplicity of positive solutions of the p-Kirchhoff problem

5_LePhuong.png 

where 6_LePhuong.pngis a smooth bounded domain of 7_LePhuong.png and 8_LePhuong.png is subcritical and positive in a right neighborhood of zero. The main feature of our problem is that 9_LePhuong.png may be any continuous function such that the integral of m in each connected component of 10_LePhuong.png is controlled by 11_LePhuong.png. Therefore, in our paper m may be degenerate, i.e., it could vanish, and sign-changing at any number of different points.