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Twin Solutions Of Even Order Boundary Value Problems For Ordinary Differential Equations And Finite Difference Equations, Xun Sun
Theses, Dissertations and Capstones
The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem
(-1)ny(2n) = f(y); n = 1; 2; 3 ... and t 2 [0; 1];
with boundary conditions
y(2k)(0) = 0
y(2k+1)(1) = 0 for k = 0; 1; 2 ... n - 1:
This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem
(-1)n (2n)u(k)g(u(k)); n = 1; 2; 3 .... and k (0; ... N);
with boundary conditions
(2k)u(0) …