-Selectors for Pairs of Oppositely Semicontinuous Multifunctions and Some Applications to Strongly Nonlinear Inclusions

  • Hong Thai Nguyen

    Szczecin University, Poland
  • M. Juniewicz

    Szczecin University, Poland
  • J. Zieminska

    Szczecin University, Poland

Abstract

We present a new approximate joint selection theorem which unifies Michael’s theorem (1956) on continuous selections and Cellina’s theorem (1969) on continuous -approximate selections. More precisely, we show that, given a convex-valued -upper semicontinuous multifunction and a convex-closed-valued lower semicontinuous multifunction with , one can find a continuous function which is both a selection of and an -approximate selection of . We also prove a parametric version of this theorem for multifunctions and of two variables where ­ is a measure space. Using this selection theorem, we obtain an existence result for elliptic systems involving a vector Laplacian and a strongly nonlinear multi-valued right-hand side, subject to Dirichlet boundary conditions.

Cite this article

Hong Thai Nguyen, M. Juniewicz, J. Zieminska, -Selectors for Pairs of Oppositely Semicontinuous Multifunctions and Some Applications to Strongly Nonlinear Inclusions. Z. Anal. Anwend. 19 (2000), no. 2, pp. 381–393

DOI 10.4171/ZAA/957