Physical Sciences and Mathematics Commons^™

Positive Solutions Of A Nonlinear N-Th Order Eigenvalue Problem, John R. Graef, Johnny Henderson, Bo Yang

Faculty and Research Publications

For 1/2 < p < 1 fixed, values of lambda > 0 are determined for which there exist positive solutions of the n-th order differential equation u((n)) = lambda g(t)f(u), 0 < t < 1, satisfying the three-point boundary conditions, u((i-1)) (0) = u((n-2)) (P) = u((n-1)) (1) = 0, 1

The problem is converted to a third order differential-integro boundary value problem and then a recent result of Graef and Yang for third order boundary value problems is adapted. An example is included to illustrate the results.

Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Beam Equation, Jun Ji, Bo Yang

Faculty and Research Publications

We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Delta(4)yi = lambda a(i+2)y(i+2), - 1= b(j), 1