scholarly journals Multiplicity results for semilinear elliptic boundary value problems in Besov and Triebel-Lizorkin spaces

1991 ◽  
Vol 34 (3) ◽  
pp. 393-410 ◽  
Author(s):  
L. Päivärinta ◽  
T. Runst
Keyword(s):  
Boundary Value Problems ◽  
Lower Bounds ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Number Of Solutions ◽  
Multiplicity Results ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic ◽  
Superlinear Elliptic Boundary

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.

Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist

2001 ◽  
Vol 131 (3) ◽  
pp. 721-732 ◽  
Author(s):  
Shujie Li ◽  
Kanishka Perera ◽  
Jiabao Su
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Elliptic Boundary Value Problems ◽  
Critical Groups ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic

We compute critical groups in semilinear elliptic boundary-value problems in which the nonlinear term may fail to have asymptotic limits at zero and at infinity. As applications, we prove several new existence results.

Sign in / Sign up

Export Citation Format

Share Document