Variational, Topological, and Partial Order Methods with Their Applications by Zhitao Zhang

Author:Zhitao Zhang
Language: eng
Format: epub, pdf
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Proof

Let , the proof is similar to that of Corollary 6.1.1. □

Remark 6.1.1

When a 12(x)≡1, a 21(x)≡1, we can use the following conditions instead of the (H 3) of Theorem 6.1.1:

then the conclusion is valid.

6.1.3 Application to Two-Point Boundary Value Problems

Consider the following ordinary differential system of equations:

(6.45)

It is well known that the solution to (6.45) in C 2[0,1]×C 2[0,1] is equivalent to the solution of the following integral system of (6.46) in C[0,1]×C[0,1]:

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