# American Institute of Mathematical Sciences

January  2013, 33(1): 255-276. doi: 10.3934/dcds.2013.33.255

## Existence and enclosure of solutions to noncoercive systems of inequalities with multivalued mappings and non-power growths

 1 Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, United States

Received  August 2011 Revised  October 2011 Published  September 2012

This paper is about systems of variational inequalities of the form: $$\left\{ \begin{array}{l} ‹A_k U_k+ F_k (u) , v_k -u_k› ≥ 0,\; ∀ v_k ∈ K_k \\ u_k ∈ K_k , \end{array} \right.$$ $(k=1,\dots , m)$, where $A_k$ and $F_k$ are multivalued mappings with possibly non-power growths and $K_k$ is a closed, convex set. We concentrate on the noncoercive case and follow a sub-supersolution approach to obtain the existence and enclosure of solutions to the above system between sub- and supersolutions.
Citation: Vy Khoi Le. Existence and enclosure of solutions to noncoercive systems of inequalities with multivalued mappings and non-power growths. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 255-276. doi: 10.3934/dcds.2013.33.255
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