Solvability of 2<em>n</em>-Order <em>m</em>-Point Boundary Value Problem at Resonance

JIANG Wei-hua; GUO Yan-ping; QIU Ji-qing

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(9): 1087-1094

JIANG Wei-hua, GUO Yan-ping, QIU Ji-qing. Solvability of 2n-Order m-Point Boundary Value Problem at Resonance[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1087-1094.

Citation:

JIANG Wei-hua, GUO Yan-ping, QIU Ji-qing. Solvability of 2n-Order m-Point Boundary Value Problem at Resonance[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1087-1094.

Citation:

JIANG Wei-hua, GUO Yan-ping, QIU Ji-qing. Solvability of 2n-Order m-Point Boundary Value Problem at Resonance[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1087-1094.

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Solvability of 2n-Order m-Point Boundary Value Problem at Resonance

1.
College of Mathematics and Science of Information, Hebei Normal University, Shijiazhuang, 050016, P. R. China;

Received Date: 2006-10-23
Rev Recd Date: 2007-07-10
Publish Date: 2007-09-15

Abstract

Abstract

The higher order multiple point boundary value problem at resonance is studied. Firstly, a Fredholm operator L with index zero and a projector operator P are defined in the subset of X and in X, respectively, such that L is invertible in the intersection of the domain of L and the kernel of P, where X is the space of functions whose (2n-1) th order derivatives are continuous. Secondly, a projector operator Q is defined in the Lebesgue integrable functions. space Y such that the composition of the inverse operator of L, I-Q and the nonlinear term f is compact, where I is the identity mapping in Y. Finally, imposing growth conditions on f, the existence of at least one solution for the 2n-order m-point boundary value problem at resonance is obtained by using coincidence degree theory of Mawhin. An example is given to demonstrate the result. The interest is that the nonlinear term f may be noncontinuous.
- resonance,
- Fredholm operator,
- multi-pointboundary value problem,
- coincidence degree theory

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References(13)

References

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