Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 17, pp. 1-29.

Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems

Chao-Nien Chen & Shyuh-yaur Tzeng

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.

Submitted December 29, 1998. Published May 14, 1999.
Math Subject Classification: 35J20, 35J25.
Key Words: elliptic equation, Palais-Smale sequence, minimax method.

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Chao-Nien Chen
Department of Mathematics
National University of Education
Changhua, Taiwan, ROC
e-mail: chenc@math.ncue.edu.tw
Shyuh-yaur Tzeng
Department of Mathematics
National University of Education
Changhua, Taiwan, ROC

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