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Abstract: The purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive Kolmogorov systems via the skew-product flows approach. It is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew-product flow associated with a nonautonomous (random) competitive Kolmogorov system. [Copyright &y& Elsevier]

Abstract: In this paper we consider the differential inclusion problemwhere is radially symmetric, and stands for the generalized gradient of a locally Lipschitz function . Under suitable oscillatory assumptions on the potential at zero or at infinity, we show the existence of infinitely many, radially symmetric solutions of (DI). No symmetry requirement on is needed. Our approach is based on a non-smooth Ricceri-type variational principle, developed by Marano and Motreanu (J. Differential Equations 182 (2002) 108–120). [Copyright &y& Elsevier]