Some Properties of Palais-Smale Sequences with Applications to Elliptic Boundary-value Problems
Date
1999-05-14
Authors
Chen, Chao-Nien
Tzeng, Shyuh-yaur
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
When 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.
Description
Keywords
elliptic equation, Palais-Smale sequence, minimax method
Citation
Chen, 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.
Rights
Attribution 4.0 International