Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations

In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations −M(∫RN∣∇v∣2dx)Δv=g(v)inRN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-M\left(\int_{\mathbb{R}^{N}}{\vert\nabla v\vert}^{2}dx\right)\Delta v=g(v) \quad {\rm in}\;{\mathbb{R}^{N}},$$\end{document} where M: [0, +∞) ↦ ℝ is a continuous function satisfying some suitable conditions and v ∈ H1(ℝN). Applying our results to the case M(t) = at + b, a, b > 0, we make it clear all the positive solutions for all dimensions N ≥ 1. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].