Chen, Chao-NienTzeng, Shyuh-yaur2019-11-122019-11-121999-05-14Chen, C. N., & Tzeng, S. Y. (1999). Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems. <i>Electronic Journal of Differential Equations, 1999</i>(17), pp. 1-29.1072-6691https://hdl.handle.net/10877/8793When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied. To overcome this difficulty, we analyze Palais-Smale sequences, and use their convergence to justify the existence of critical points for a functional. We show the existence of positive solutions using a minimax method and comparison arguments for semilinear elliptic equations.Text29 pages1 file (.pdf)enAttribution 4.0 Internationalelliptic equationPalais-Smale sequenceminimax methodArticle