scholarly journals An extension of the Rabinowitz bifurcation theorem to Lipschitz potential operators in Hilbert spaces

1997 ◽  
Vol 125 (9) ◽  
pp. 2725-2732 ◽  
Author(s):  
Alexander Ioffe ◽  
Efim Schwartzman
Keyword(s):  
Hilbert Spaces ◽  
Bifurcation Theorem ◽  
Potential Operators

scholarly journals Fixed point theorems for compact potential operators in Hilbert spaces

2017 ◽  
Vol 18 (2) ◽  
pp. 493-502
Author(s):  
A. Boucenna ◽  
◽  
S. Djebali ◽  
T. Moussaoui ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Potential Operators

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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