Dependence of eigenvalues of fourth-order boundary value problems with transmission conditions
Bertin Zinsou
Abstract
A general fourth-order regular ordinary differential equation with eigenvalue dependent boundary conditions and transmission conditions are considered. We prove that the eigenvalues depend continuously and smoothly on the coefficients of the differential equation and on the boundary and transmission matrices. We provide as well formulas for the derivatives with respect to each of these parameters.
Topics & Concepts
MathematicsEigenvalues and eigenvectorsBoundary value problemMatrix differential equationMathematical analysisOrdinary differential equationTransmission (telecommunications)Differential equationOrder (exchange)Boundary valuesApplied mathematicsElectrical engineeringPhysicsQuantum mechanicsEngineeringEconomicsFinanceDifferential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsNumerical methods for differential equations