Variational Approaches to Kirchhoff-Type Second-Order Impulsive Differential Equations on the Half-Line

In this work we continue the study of the multiplicity results for a Kirchhoff-type second-order impulsive differential equation on the half-line. In fact, using a consequence of the local minimum theorem due Bonanno we look into the existence one solution under algebraic conditions on the nonlinear term and two solutions for the problem under algebraic conditions with the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing two critical point theorems, one due Averna and Bonanno, and another one due Bonanno we guarantee the existence of two and three solutions for the problem in a special case.