A Unified Approach to Estimation of Lower Bounds for the First Eigenvalue of Several Elliptic Boundary Value Problems

1987 ◽  
Vol 131 (1) ◽  
pp. 183-199 ◽  
Author(s):  
Klaus Gürlebeck ◽  
Wolfgang Sprössig
Keyword(s):  
Boundary Value Problems ◽  
Lower Bounds ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
First Eigenvalue ◽  
Unified Approach ◽  
Elliptic Boundary Value ◽  
The First Eigenvalue

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.

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