Article Contents
Article Contents

# The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations

• Assume that the unperturbed parabolic equation has a degenerate homoclinic orbit. Under $T$-periodic perturbations, the periodic solutions bifurcated from the homoclinic solution are studied. By Fredholm alternative and Lyapunov-Schmidt reduction, the bifurcation functions defined between two finite-dimensional spaces are obtained. Some solvable conditions for the bifurcation functions are given. It is shown that, for any large $n>0$, the perturbed parabolic differential equation has a periodic solution with period $nT$.
Mathematics Subject Classification: Primary: 34C23, 34C25; Secondary: 34C45, 34C40.

 Citation:

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