Linking Methods for Componentwise Variational Systems


The paper deals with the equilibrium solutions of two-equation systems in which each component equation has a variational structure. Solutions are obtained that can be in one of the following generalized Nash situations: (a) one component of the solution represents a mountain pass type critical point and the other is a minimizer; (b) both components of the solution are mountain pass type; (c) both components are minimizers, that is, the solution is a proper Nash equilibrium. The simultaneous treatment of critical points of the mountain pass type and of the minimum ones is achieved by using a unifying notion of linking. The theory is applied to a system of four elliptic equations in which the subsystems formed by the first two and the last two equations, respectively, are of gradient type. An example shows that the conditions found are non-contradictory. The theory could be applied to other classes of systems.


Radu Precup
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, Cluj-Napoca, Romania Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Andrei Stan
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania


Variational method; linking; critical point; mountain pass geometry; Nash type equilibrium; monotone operator; elliptic system

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R. Precup, A. Stan, Linking methods for componentwise variational systems, Results Math. 78 (2023) 246,



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