Superlinear elliptic boundary value problems

1995 ◽  
Vol 86 (1) ◽  
pp. 253-265 ◽  
Author(s):  
Martin Schechter

2006 ◽  
Vol 6 (2) ◽  
Author(s):  
Mónica Clapp ◽  
Eric Hernández-Martínez

AbstractWe study superlinear elliptic boundary value problems with perturbed symmetries in domains which are invariant under the action of a group G. We give conditions on the growth of the nonlinearity which guarantee the existence of infinitely many G-invariant solutions. These conditions improve those obtained by Bahri and Lions (1988) and Bolle, Ghoussoub and Tehrani (2000) if the domain contains a G-orbit of large enough dimension.





1991 ◽  
Vol 34 (3) ◽  
pp. 393-410 ◽  
Author(s):  
L. Päivärinta ◽  
T. Runst

The paper deals with superlinear elliptic boundary value problems depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we prove lower bounds on the number of solutions. The results generalize a theorem due to Lazer and McKenna within the framework of quasi-Banach spaces of Besov and Triebel-Lizorkin spaces.







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