### Periodic solutions of a class of integral equations

DOI: http://dx.doi.org/10.12775/TMNA.2003.038

#### Abstract

Based on the fixed point index theory for a Banach space, nontrivial

periodic solutions are found for a class of integral equation of the form

$$

\phi (x)=\int_{[x,x+\omega ]\cap \Omega }K(x,y)f(y,\phi (y-\tau (y)))dy,

\quad

x\in \Omega ,

$$

where $\Omega $ is a closed subset of $\mathbb R^{N}$ with perioidc structure.

periodic solutions are found for a class of integral equation of the form

$$

\phi (x)=\int_{[x,x+\omega ]\cap \Omega }K(x,y)f(y,\phi (y-\tau (y)))dy,

\quad

x\in \Omega ,

$$

where $\Omega $ is a closed subset of $\mathbb R^{N}$ with perioidc structure.

#### Keywords

Perioidc solution; fixed point index

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