USA-Chile Workshop on Nonlinear Analysis,

Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 101-107.

### An abstract existence result and its applications

Sui Sun Cheng, Bin Liu, & Jian-She Yu

**Abstract:**

By means of Borsuk's theorem and continuation through an
admissible homotopy, we establish an existence theorem for
operator equation with homogeneous nonlinearity. We illustrate our
theorem by considering a perturbed functional differential
equation under periodic boundary conditions.
Published January 8, 2001.

Math Subject Classifications: 34K10, 34C20.

Key Words: Borsuk's theorem, Fredholm mapping,
perturbed differential equation, periodic solution.

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Sui Sun Cheng

Department of Mathematics, Tsing Hua University

Taiwan 30043, R. O. China

e-mail: sscheng@math.nthu.edu.tw
Bin Liu

Department of Mathematics, Hubei Normal Univeristy

Huangshi, Hubei 435002, P. R. China

Jian-She Yu

Department of Applied Mathematics, Hunan University

Changsha, Hunan 410082, P. R. China

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