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Dependence on parameters for nonlinear equations -- abstract principles and applications
  • Michał Bełdziński,
  • Marek Galewski,
  • Igor Kossowski
Michał Bełdziński
Lodz University of Technology Faculty of Technical Physics Information Technology and Applied Mathematics
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Marek Galewski
Lodz University of Technology Faculty of Technical Physics Information Technology and Applied Mathematics
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Igor Kossowski
Lodz University of Technology Faculty of Technical Physics Information Technology and Applied Mathematics
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Abstract

We provide parameter dependent version of the Browder–Minty Theorem in case when the solution is unique utilizing different types of monotonicity and compactness assumptions related to condition (S)2. Potential equations and the convergence of their Euler action functionals is also investigated. Applications towards the dependence on parameters for both potential and non-potenial nonlinear Dirichlet boundary problems are given.

Peer review status:UNDER REVIEW

14 Jun 2021Submitted to Mathematical Methods in the Applied Sciences
16 Jun 2021Submission Checks Completed
16 Jun 2021Assigned to Editor
22 Jun 2021Reviewer(s) Assigned
14 Sep 2021Review(s) Completed, Editorial Evaluation Pending
15 Sep 2021Editorial Decision: Revise Minor
15 Sep 20211st Revision Received
16 Sep 2021Submission Checks Completed
16 Sep 2021Assigned to Editor
16 Sep 2021Review(s) Completed, Editorial Evaluation Pending