Nontrivial solutions of Kirchhoff type problems

In this work, we study Kirchhoff type problems on a bounded domain. We consider the cases where the nonlinearity is superlinear near zero but asymptotically 4 -linear at infinity, and the nonlinearity is asymptotically linear near zero but 4 -superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.