Geodesic
Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems
Electronic journal of differential equations, Tome 1999 (1999)
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.
Classification : 35J20, 35J25
Keywords: elliptic equation, palais-Smale sequence, minimax method 
@article{EJDE_1999__1999__a59,
     author = {Chen,  Chao-Nien and Tzeng,  Shyuh-yaur},
     title = {Some properties of {Palais-Smale} sequences with applications to elliptic boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0921.35045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a59/}
}
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Chen,  Chao-Nien; Tzeng,  Shyuh-yaur. Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a59/