Existence and uniqueness of minimizers for <i>L</i><sup>2</sup>‐constrained problems related to fractional Kirchhoff equation
Xiaomeng Huang, Yimin Zhang
Abstract
In this paper, we discuss the existence and uniqueness of solutions of the constrained variational problem with respect to the fractional Kirchhoff equation. For the exponent p < p * ( s , N ), a complete classification with respect to p for the existence of solutions of the fractional Kirchhoff functional on the L 2 ‐normalized manifold was given. Furthermore, all these solutions are unique up to translations, and our methods depend only on some simple energy estimates.
Topics & Concepts
UniquenessMathematicsMathematical analysisSimple (philosophy)ExponentManifold (fluid mechanics)Energy (signal processing)Applied mathematicsPure mathematicsEpistemologyLinguisticsPhilosophyStatisticsEngineeringMechanical engineeringNonlinear Partial Differential EquationsStability and Controllability of Differential EquationsAdvanced Mathematical Physics Problems