Poincare inequalities in reflexive cones


We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter’s localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray–Schauder boundary condition is also involved.


Petru Jebelean
West University of Timişoara, Department of Mathematics, Timişoara, Romania

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


Reflexive cone; Compact embedding; Trace operator; Boundary value problem; A priori bounds

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P. Jebelean, R. Precup, Poincare inequalities in reflexive cones, Appl. Math. Letters 24 (2011), 359-363, http://dx.doi.org/10.1016/j.aml.2010.10.024


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