Rate processes with dynamical disorder: A direct variational approach

2006 ◽  
Vol 124 (20) ◽  
pp. 204111 ◽  
Author(s):  
Ananya Debnath ◽  
Rajarshi Chakrabarti ◽  
K. L. Sebastian
Keyword(s):  
Variational Approach ◽  
Rate Processes ◽  
Dynamical Disorder

Rate processes with dynamical disorder

1990 ◽  
Vol 23 (5) ◽  
pp. 148-152 ◽  
Author(s):  
Robert Zwanzig
Keyword(s):  
Rate Processes ◽  
Dynamical Disorder

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

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