This article is cited in 3 papers

Reduction of variational inequalities with irregular operators on a ball to regular operator equations

M. Yu. Kokurin

Chair of Mathematical Analysis and Function Theory, Mari State University, Ioshkar Ola, Russia

Abstract: We propose a method for reducing variational inequalities defined by general smooth irregular operators on a ball in a Hilbert space to equivalent regular operator equations. The mentioned equations involve the operator of metric projection on the boundary of the ball. We establish conditions which guarantee the local strong monotonicity of the obtained equations. We discuss applications to the problem of finding normed eigenvectors of nonlinear operators.

Keywords: variational inequality, smooth operator, irregular operator, operator equation, eigenvector.

UDC: 517.988

Received: 02.02.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:4, 26–34

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