Nonlinear elliptic fourth order equations existence and multiplicity results
Mohammed Benalili, Kamel Tahri

TL;DR
This paper investigates the existence and multiplicity of solutions for a class of nonlinear fourth order elliptic equations using critical point theory, demonstrating the existence of three solutions in the constant coefficient case.
Contribution
It introduces a novel application of critical point theory to fourth order nonlinear elliptic equations and establishes the existence of multiple solutions for constant coefficient cases.
Findings
Existence of solutions established for the class of equations.
Three distinct solutions found in the constant coefficient case.
Solutions characterized as critical points of a restricted functional.
Abstract
This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a suitable manifold.In the case of constant coefficients we obtain the existence of tree distinct solutions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis
