Journal of Mathematical Analysis and Applications
The existence of positive solutions depending on a nonnegative parameter lambda 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. (C) 2013 Elsevier Inc. All rights reserved.
Li, Y., Li, F., & Shi, J. (2014). Existence of positive solutions to Kirchhoff type problems with zero mass. Journal of Mathematical Analysis and Applications, 410(1), 361-374.