Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System

WANG Fang-lei; AN Yu-kun

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WANG Fang-lei, AN Yu-kun. Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System[J]. Applied Mathematics and Mechanics, 2009, 30(1): 83-89.

Citation:

WANG Fang-lei, AN Yu-kun. Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System[J]. Applied Mathematics and Mechanics, 2009, 30(1): 83-89.

Citation:

WANG Fang-lei, AN Yu-kun. Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System[J]. Applied Mathematics and Mechanics, 2009, 30(1): 83-89.

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Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China

Received Date: 2007-12-10
Rev Recd Date: 2008-11-11
Publish Date: 2009-01-15

Abstract

Abstract

There exist at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, using the Green function and maximum principle, the existence of solutions of nonlinear telegraph system was equivalent to the existence of fixed points of an operator. Finally, imposing growth conditions on the nonlinearities, the existence of at least three fixed points in cone was obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces, namely, there exist at least three positive doubly periodic solutions of the nonlinear telegraph system.
- telegraph system,
- doubly periodic solution,
- cone,
- fixed point theorem

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References(12)

References

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