Existence of nontrivial solutions for a class of nonlocal Kirchhoff type problems

Abstract

Abstract With the aid of the three-critical-point theorem due to Brezis and Nirenberg (see Brezis and Nirenberg in Commun. Pure Appl. Math. 44:939–963, 1991), two existence results of at least two nontrivial solutions for a class of nonlocal Kirchhoff type problems are obtained.

Keywords

• Kirchhoff type problem
• ( P S ) $(PS)$ condition
• Local linking
• Critical point