Periodic solutions of a class of integral equations

Shugui Kang, Guang Zhang, Sui Sun Cheng

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.

Keywords


Perioidc solution; fixed point index

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