Existence of positive solutions to Kirchhoff type problems with zero mass

The existence of positive solutions depending on a nonnegative parameter λ to Kirchhoff type problems with zero mass is proved by using variational method, and the new result does not require usual compactness conditions. A priori estimate and a Pohozaev type identity are used to obtain the bounded Palais–Smale sequences for constant coefficient nonlinearity, while a cut-off functional and Pohozaev type identity are utilized to obtain the bounded Palais–Smale sequences for the variable-coefficient case.