Semi-classical solutions for Kirchhoff type problem with a critical frequency

In the present paper, we consider the following Kirchhoff type problem -(epsilon(2) + epsilon b integral(R3) vertical bar del v vertical bar(2))Delta v + V(x) =vertical bar v vertical bar(p-2)v in R-3, where b > 0, p is an element of (4,6), the potential V is an element of C(R-3,R) and e is a positive parameter. The existence and multiplicity of semi-classical state solutions are obtained by variational method for this problem with several classes of critical frequency potentials, i.e., inf(R)N V = 0. As to Kirchhoff type problem, little has been done for the critical frequency cases in the literature, especially the potential may vanish at infinity.

Automated summary

This paper examines the existence and multiplicity of solutions for Kirchhoff type problems under different conditions, especially focusing on the critical frequency cases. Little research has been done on these cases in the literature, particularly when the potential may vanish at infinity.