LAUSR

The problem of homoclinic solutions is considered for a singular Rayleigh equation $$\begin{aligned} x''(t)+f(x'(t))-g(x(t))-\frac{\alpha (t)x(t)}{1-x(t)}=h(t), \end{aligned}$$ x ′ ′ ( t ) + f ( x ′ ( t ) ) - g ( x ( t ) ) - α ( t ) x ( t ) 1 - x ( t ) = h ( t ) , where $$f,g,h,\alpha : R\rightarrow R$$ f , g , h , α : R → R are continuous and $$\alpha (t)$$ α ( t ) is $$T-$$ T - periodic. By using a continuation theorem of coincidence degree principle, some new results on the existence and uniqueness of homoclinic solution to the equation are obtained.