Johnny Henderson

Inequalities based on a generalization of concavity

The concept of concavity is generalized to functions, y, satisfying nth order differential inequalities, (-I)n-ky(n)(t) > 0,0 IIyIi/4m, 1/4 0,0 IIYII/4, where Il = supo 2 is an integer, k E {1, ... , n 1}, and if (2) (l)n-k)y(n) > 0, 0 < t < 1, t3f YW (0 0, j,*** .. , 1Y(j O,j 1 . ,kthen for 1/4 < t < 3/4,

Comparison of eigenvalues for a class of two-point boundary value problems

The theory of u 0-positive operators with respect to a cone in a Banach space is applied to a class of two-point boundary value problems for ordinary differential equations. The existence of a smallest positive eigenvalue is established, and then a comparison theorem for smallest positive eigenvalues is obtained.

Multipoint boundary value problems with parameter for a system of difference equations

Solutionsu(t), of the first order system of difference equations u(t p 1) e f(t,u(t),λ) satisfying the multipoint boundary conditions ,are differentiated with respect to the components of r and with respect to the components of the parameter λ, where are constant real n×n matrices

Nonlinear interpolation and boundary value problems

Compactness Criterion for Solutions of Nonlinear Differential Equations Conjugate and Right Focal Boundary Value Problems Nonlocal Boundary Value Problems Boundary Value Problems for Finite Difference Equations Boundary Value Problems for Dynamic Equations on Time Scales