Multiple periodic solutions and positive homoclinic solution for a differential equation (Q372714)

The authors consider the nonautonomous differential equation NEWLINE\[NEWLINEx''-a(t)x+b(t)x^2+c(t)x^3=0,NEWLINE\]NEWLINE where \(a,b\) and \(c\) are continuous \(T\)-periodic functions and obtain two results for them. The first one gives, under certain additional hypotheses, the existence of at least two nontrivial \(T\)-periodic solutions. The main tool for the proof is the use of coincidence degree. The second result provides sufficient conditions for the existence of positive homoclinic solutions, i.e. positive solutions satisfying \(x(\pm\infty)=x'(\pm\infty)=0\).