Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current
Jifeng Chu, Kateryna Marynets
Abstract
Abstract The aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.
Topics & Concepts
Circumpolar starSublinear functionNonlinear systemMathematicsEigenvalues and eigenvectorsClass (philosophy)Current (fluid)Mathematical analysisDifferential equationFixed pointBoundary value problemFixed-point indexApplied mathematicsPure mathematicsGeologyPhysicsComputer scienceOceanographyArtificial intelligenceQuantum mechanicsDifferential Equations and Numerical MethodsNonlinear Partial Differential EquationsNonlinear Differential Equations Analysis