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Localization properties for nonlinear equations involving monotone operators
  • M. GalewskiOrcid
M. Galewski
Lodz University of Technology
Author Profile

Peer review status:ACCEPTED

13 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
20 Mar 2020Submission Checks Completed
20 Mar 2020Assigned to Editor
20 Mar 2020Reviewer(s) Assigned
03 Jun 2020Review(s) Completed, Editorial Evaluation Pending
04 Jun 2020Editorial Decision: Revise Minor
05 Jun 20201st Revision Received
05 Jun 2020Submission Checks Completed
05 Jun 2020Assigned to Editor
05 Jun 2020Editorial Decision: Accept


Using monotonicity methods, the Lagrange multiplier rule and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper.