Qingkai Kong

Oscillation theory for functional differential equations

Preliminaries oscillations of first order delay differential equations oscillation of first order neutral differential equations oscillation and nonoscillation of second order differential equations with deviating arguments oscillation of higher order neutral differential equations oscillation of systems of neutral differential equations boundary value problems for second order functional differential equations.

Boundary value problems for singular second-order functional differential equations

Abstract We consider general linear boundary value problems for equations of the form y′ + f ( x, y (τ( x )) = 0, 0 x x ) is continuous and f ( x, y ) has a singularity at y = 0. The results improve and extend earlier results for the case τ( x ) = x , due to Taliaferro (1979) and Gatica. (1989).

UNIQUENESS OF POSITIVE SOLUTIONS OF FRACTIONAL BOUNDARY VALUE PROBLEMS WITH NON-HOMOGENEOUS INTEGRAL BOUNDARY CONDITIONS

The authors study a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions. The existence and uniqueness of positive solutions are discussed. An example is given as the application of the results.

POSITIVE SOLUTIONS OF HIGHER-ORDER BOUNDARY-VALUE PROBLEMS

We consider a class of even-order boundary-value problems with nonlinear boundary conditions and an eigenvalue parameter

Positive solutions of boundary value problems for third-order functional difference equations

\lambda

Sturm-Liouville Problems Whose Leading Coefficient Function Changes Sign

in the equations. Sufficient conditions are obtained for the existence and non-existence of positive solutions of the problems for different values of

Fractional boundary value problems with integral boundary conditions

\lambda

Interval criteria for forced oscillation with nonlinearities given by Riemann–Stieltjes integrals

.

Nonoscillation of a class of neutral differential equations

The existence of positive solutions are established for the third-order functional difference equation Δ3u(n) + a(n)f(n, u(w(n))) = 0, 0 ≤ n ≤ T, satisfying u(n) = φ(n), n1 ≤ n ≤ 1, and u(n) = ψ(n), T + 3 ≤ n ≤ n2, with φ(0) = φ(1) = ψ(T + 3) = 0. The results in this paper generalize and substantially improve recent work by Agarwal and Henderson on boundary value problems related to third-order difference equations.

Positive Solutions of Nonlinear m-point Boundary Value Problems on a Measure Chain

Fora givenSturm-Liouville equation whoseleading coefficient function changessign, we es- tablish inequalities among the eigenvalues for any coupled self-adjoint boundary condition and those for two corresponding separated self-adjoint boundary conditions. By a recent result of Binding and Volkmer, the eigenvalues(unbounded from both below and above) for a separated self-adjoint bound- ary condition can be numbered in terms of the Prangle; and our inequalities can then be used to index the eigenvalues for any coupled self-adjoint boundary condition. Under this indexing scheme, we determine the discontinuities of each eigenvalue as a function on the space of such Sturm-Liouville problems, and its range as a function on the space of self-adjoint boundary conditions. We also re- late this indexing scheme to the number of zeros of eigenfunctions. In addition, we characterize the discontinuities of each eigenvalue under a different indexing scheme.