scholarly journals The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces

2005 ◽  
Vol 214 (1) ◽  
pp. 189-231 ◽  
Author(s):  
Athanassios G. Kartsatos ◽  
Igor V. Skrypnik ◽  
Vladimir N. Shramenko
Keyword(s):  
Critical Point ◽  
Banach Spaces ◽  
Elliptic Operators ◽  
Reflexive Banach Spaces

scholarly journals Nontrivial solutions for a multivalued problem with strong resonance

1996 ◽  
Vol 38 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Vicenţiu D. Rădulescu
Keyword(s):  
Critical Point ◽  
Banach Spaces ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Mountain Pass ◽  
Nontrivial Solutions ◽  
Reflexive Banach Spaces ◽  
Strong Resonance ◽  
Locally Lipschitz ◽  
Critical Point Theorems

The Mountain-Pass Theorem of Ambrosetti and Rabinowitz (see [1]) and the Saddle Point Theorem of Rabinowitz (see [21]) are very important tools in the critical point theory of C1-functional. That is why it is natural to ask us what happens if the functional fails to be differentiable. The first who considered such a case were Aubin and Clarke (see [6]) and Chang (see [12]),who gave suitable variants of the Mountain-Pass Theorem for locally Lipschitz functionals which are denned on reflexive Banach spaces. For this aim they replaced the usual gradient with a generalized one, which was firstly defined by Clarke (see [13], [14]).As observed by Brezis (see [12, p. 114]), these abstract critical point theorems remain valid in non-reflexive Banach spaces.

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