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Start Over Subject critical point theory

1. A nontrivial solution for Neumann noncoercive hemivariational inequalities

Creator:
Halidias, Nikolaos
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
noncoercive hemivariational inequality, critical point theory, nontrivial solution, and locally Lipschitz functionals
Language:
English
Description:
In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Nonlinear boundary value problems involving the extrinsic mean curvature operator

Creator:
Mawhin, Jean
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
extrinsic mean curvature operator, Dirichlet problem, radial solution, positive solution, Leray-Schauder degree, and critical point theory
Language:
English
Description:
The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type ∇ · ( ∇v ⁄ √ 1 − |∇v| 2 ) = f(|x|, v) in BR, u = 0 on ∂BR, where BR is the open ball of center 0 and radius R in R n , and f is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Positive fixed point theorems arising from seeking steady states of neural networks

Creator:
Wang, Gen-Qiang and Cheng, Sui Sun
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
positive fixed point, neural network, periodic solution, difference equation, discrete boundary condition, and critical point theory
Language:
English
Description:
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The derivation is based on elementary analysis. However, it is hoped that our easy fixed point theorems have potential applications in exploring stationary states of similar biological network models.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public