On positive ground state solutions for the nonlinear Kirchhoff type equations in ℝ3

Abstract

In this article, we first give a much more concise proof on the existence of ground state solutions of Kirchhoff equation by rearrangement than that given in Li and Ye [Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3. J. Differ. Equat. 2014;257(2):566-600] and Ye [Positive high energy solution for Kirchhoff equation in R3 with superlinear nonlinearities via Nehari–Pohozaev manifold. Discrete Contin. Dyn. Syst. 2015;35(8):3857-3877], where a,b>0,2<p<5. And then, we prove a nonexistence result on ground state solutions of the non-autonomous Kirchhoff equation which can be considered as a nice complement to Zhang et al. [Semiclassical ground states for a class of nonlinear Kirchhoff-type problems. Appl. Anal. 2016;96(13):2267-2284].