Variational properties of the solutions for second-order differential equations and systems on semi-line

Abstract

In this article, an abstract theory regarding variational properties of the fixed points of contractions and Perov contractions is applied to boundary value problems on semi-line for second-order differential equations and systems. The main result states that under suitable conditions the unique solution of such a system is a Nash-type equilibrium of the corresponding energy functionals.

Authors

Adela Novac
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Boundary value problems on infinite intervals; Critical points; Fixed points; Nash-type equilibrium.

Paper coordinates

A. Novac, R. Precup, Variational properties of the solutions for second-order differential equations and systems on semi-line, Numer. Funct. Anal. Optim. 36 (2015), 930-941, https://doi.org/10.1080/01630563.2015.1041144

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About this paper

Journal

Numerical Functional Analysis and Optimization

Publisher Name

Taylor and Francis Ltd.

Print ISSN

01630563

Online ISSN

15322467

google scholar link

[1] R. P. Agarwal and D. O’Regan ( 2001 ). Infinite Interval Problems for Differential, Difference and Integral Equations . Kluwer Academic , Dordrecht . [Crossref][Google Scholar]
[2]
H. Brezis ( 1983 ). Analyse fonctionnelle. Théorie et applications . Masson , Paris . [Google Scholar]
[3]
A. Budescu ( 2014 ). Semilinear operator equations and systems with potential-type nonlinearities . Studia Univ. Babeş-Bolyai Math. 59 : 199 – 212 . [Google Scholar]
[4]
M. Frigon and D. O’Regan ( 2003 ). Fixed points of cone-compressing and cone-extending operators in Fréchet spaces . Bull. London Math. Soc. 35 : 672 – 680 . [Crossref][Web of Science ®][Google Scholar]
[5]
T. H. Fay and S. D. Graham ( 2003 ). Coupled spring equations . Int. J. Math. Educ. Sci. Technol. 34 : 65 – 79 . [Taylor & Francis Online][Google Scholar]
[6]
H. Lian and W. Ge ( 2006 ). Existence of positive solutions for Sturm–Liouville boundary value problems on the half-line . J. Math. Anal. Appl. 321 : 781 – 792 . [Crossref][Web of Science ®][Google Scholar]
[7]
J. D. Murray ( 1989 ). Mathematical Biology . Springer , New York . [Crossref][Google Scholar
[8]
D. O’Regan ( 1996 ). Continuation fixed point theorems for locally convex linear topological spaces . Math. Comput. Modelling 24 : 57 – 70 . [Crossref][Web of Science ®][Google Scholar]
[9]
A. I. Perov ( 1964 ). On Cauchy problem for a system of ordinary differential equations . Pviblizhen. Met. Reshen. Differ. Uravn. 2 : 115 – 134 . (In Russian)  [Google Scholar]
[10]
A. I. Perov and A. V. Kibenko ( 1966 ). On a certain general method for investigation of boundary value problems . Izv. Akad. Nauk SSSR 30 : 249 – 264 . (In Russian)  [Google Scholar]
[11]
R. Precup ( 2002 ). Methods in Nonlinear Integral Equations . Springer , Amsterdam . [Crossref][Google Scholar]
[12]
R. Precup ( 2014 ). Nash-type equilibria and periodic solutions to nonvariational systems . Adv. Nonlinear Anal. 3 : 197 – 207 . [Web of Science ®][Google Scholar]

2015

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