A saddle-point theorem for strongly and weakly convex functions

2011 ◽  
Vol 75 (1) ◽  
pp. 73-100 ◽  
Author(s):  
Grigorii E Ivanov
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Convex Functions ◽  
Saddle Point Theorem ◽  
Weakly Convex

scholarly journals Existence and multiplicity of solutions for class of Navier boundary $p$-biharmonic problem near resonance

2014 ◽  
Vol 32 (2) ◽  
pp. 83 ◽  
Author(s):  
Mohammed Massar ◽  
EL Miloud Hssini ◽  
Najib Tsouli
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Saddle Point Theorem ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Near Resonance

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.

A SADDLE-POINT THEOREM

1980 ◽  
pp. 123-126
Author(s):  
Peter W. Bates ◽  
Ivar Ekeland
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Saddle Point Theorem

A Matching Theorem in GFC-Spaces with Application to Saddle Points

2013 ◽  
Vol 734-737 ◽  
pp. 2867-2870
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Saddle Point ◽  
Point Theorem ◽  
Saddle Points ◽  
Minimax Inequality ◽  
Saddle Point Theorem ◽  
Matching Theorem

In this paper, a matching theorem for weakly transfer compactly open valued mappings is established in GFC-spaces. As applications, a fixed point theorem, a minimax inequality and a saddle point theorem are obtained in GFC-spaces. Our results unify, improve and generalize some known results in recent reference.

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