Two-Point Boundary Value Problems for Duffing Equations across Resonance |
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| Authors: | X J Chang Q D Huang |
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| Institution: | (1) Institute of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China;(2) College of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China |
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| Abstract: | In this paper, we consider the equation y″+f(x,y)=0 with a nonresonance condition of the form A≤f
y
(x,y)≤B, where (k−1)2<A≤k
2<⋅⋅⋅<m
2≤B<(m+1)2, k,m∈ℤ+. With optimal control theory and the Schauder fixed-point theorem, by introducing a new cost functional, we obtain a new
existence and uniqueness result for the above equation with two-point boundary-value conditions.
This work was supported by NSFC Grant 10501017 and 985 Project of Jilin University. |
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| Keywords: | Boundary-value problems Duffing equation Resonance Optimal control Schauder fixed-point theorem |
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