Existence of positive solutions to Kirchhoff type problems with zero mass |
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Authors: | Yuhua Li Fuyi Li Junping Shi |
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Institution: | 1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China;2. Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA |
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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. |
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Keywords: | Kirchhoff type problem Zero mass Variational method Cut-off functional |
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