Preliminaries on the Fredholm Alternative Principle

2021 ◽  
pp. 175-177
Author(s):  
Matteo Dalla Riva ◽  
Massimo Lanza de Cristoforis ◽  
Paolo Musolino
Keyword(s):  
Fredholm Alternative ◽  
Alternative Principle

scholarly journals Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hailong Zhu ◽  
Shengjun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Multiplicity Results ◽  
Second Order Differential Equations ◽  
Existence And Multiplicity ◽  
Nonlinear Alternative ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Alternative Principle

The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.

scholarly journals On a boundary value problem for scalar linear functional differential equations

2004 ◽  
Vol 2004 (1) ◽  
pp. 45-67 ◽  
Author(s):  
R. Hakl ◽  
A. Lomtatidze ◽  
I. P. Stavroulakis
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Homogeneous Equation ◽  
Functional Differential Equations ◽  
Solution Space ◽  
Fredholm Alternative ◽  
Linear Boundary ◽  
Bounded Operators ◽  
Functional Differential ◽  
Linear Boundary Value Problem

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problemu′(t)=ℓ(u)(t)+q(t),h(u)=c, whereℓ:C([a,b];ℝ)→L([a,b];ℝ)andh:C([a,b];ℝ)→ℝare linear bounded operators,q∈L([a,b];ℝ), andc∈ℝ, are established even in the case whenℓis not astrongly boundedoperator. The question on the dimension of the solution space of the homogeneous equationu′(t)=ℓ(u)(t)is discussed as well.

scholarly journals Recurrent equations with sign and Fredholm alternative

2016 ◽  
Vol 9 (4) ◽  
pp. 959-977 ◽  
Author(s):  
Juan Campos ◽  
◽  
Rafael Obaya ◽  
Massimo Tarallo ◽  
◽  
...  
Keyword(s):  
Fredholm Alternative

scholarly journals Intensive home treatment, admission rates and use of mental health legislation

2010 ◽  
Vol 34 (12) ◽  
pp. 522-524 ◽  
Author(s):  
Naida F. Forbes ◽  
Helen T. Cash ◽  
Stephen M. Lawrie
Keyword(s):  
Mental Health ◽  
Home Treatment ◽  
Treatment Team ◽  
Admission Rates ◽  
Duration Of Hospital Stay ◽  
Mental Health Legislation ◽  
Local Impact ◽  
Health Legislation ◽  
Least Restrictive Alternative ◽  
Alternative Principle

Aims and methodWe examined the local impact of introducing a home treatment team on the use of in-patient psychiatric resources and rates of detention under the Mental Health (Care and Treatment) (Scotland) Act 2003.ResultsRates of admission to hospital and duration of hospital stay were unchanged. However, there was an increase in episodes of detention in the year following the team's introduction.Clinical implicationsOffering home treatment as an alternative to in-patient care may be associated with an increase in compulsory treatment. If true, this is incompatible with the ‘least restrictive alternative’ principle of the recently revised mental health legislation.

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