scholarly journals Coupling of homotopy and the variational approach for a conservative oscillator with strong odd-nonlinearity

2012 ◽  
Vol 19 (3) ◽  
pp. 417-422 ◽  
Author(s):  
Y. Khan ◽  
M. Akbarzade ◽  
A. Kargar
Keyword(s):  
Variational Approach ◽  
Conservative Oscillator ◽  
Odd Nonlinearity

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].

scholarly journals A new variational approach for the thermodynamic topology optimization of hyperelastic structures

2020 ◽  
Author(s):  
Philipp Junker ◽  
Daniel Balzani
Keyword(s):  
Topology Optimization ◽  
Variational Approach ◽  
Large Deformations ◽  
Mathematical Structure ◽  
Detailed Model ◽  
Novel Approach ◽  
Extremal Principles ◽  
Model Derivation ◽  
Numerical Discretization ◽  
Total Structure

AbstractWe present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density and total structure volume are fulfilled analytically which simplifies the numerical implementation significantly; (3) it possesses a mathematical structure that allows for a variety of numerical procedures to solve the problem of topology optimization without distinct optimization routines. We present a detailed model derivation including the chosen numerical discretization and show the validity of the approach by simulating two boundary value problems with large deformations.

scholarly journals A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Mushtaq Ahmad Khan ◽  
Asmat Ullah ◽  
Sahib Khan ◽  
Murtaza Ali ◽  
Sheraz Khan ◽  
...  
Keyword(s):  
Image Restoration ◽  
Fractional Order ◽  
Variational Approach ◽  
Fuzzy Membership
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