Variational properties of the solutions of singular second-order differential equations and systems

Abstract

This paper is devoted to the existence and variational characterization of the weak solutions of the Dirichlet boundary value problem for singular second-order ordinary differential equations and systems. The solution appears as a minimizer of the energy functional associated with the equation, and in the case of systems, as a Nash-type equilibrium of the set of energy functionals. The results are connected with the recent abstract fixed point theory due to the second author and with its application, given by the first author, to semilinear operator problems of Michlin type.

Authors

Angela Budescu
Department of Mathematics, Babeş-Bolyai University, Cluj, Romania

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

Keywords

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Paper coordinates

A. Budescu, R. Precup, Variational properties of the solutions of singular second-order differential equations and systems, J. Fixed Point Theor. Appl. 18 (2016), 505-518, https://doi.org/10.1007/s11784-016-0284-1

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About this paper

Journal

Journal of Fixed Point Theory and Applications

Publisher Name

Springer

Print ISSN

16617738

Online ISSN

16617746

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