Existence of positive solutions to Kirchhoff type problems with zero mass

By Yuhua Li, Fuyi Li, Junping Shi. 2014

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Abstract 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/05c88547fb8010d25b7330523055eec5afab87ec