Infinitely many homoclinic orbits of second-order \(p\)-Laplacian systems (Q373722)

Using the symmetric mountain pass theorem, the authors obtain new sufficient conditions for the existence of infinitely many homoclinic orbits for the second-order ordinary systems involving the \(p\)-Laplacian NEWLINE\[NEWLINE\frac{d}{dt}(|\dot u(t)|^{p-2}\dot u(t)) - a(t)|u(t)|^{p-2}u(t) + \nabla W(t,u(t)) = 0,NEWLINE\]NEWLINE where \(p > 1\), \(a\) is continuous and \(W\) of class \(C^1\). Previous results of P.\,H.\thinspace Rabinowitz and M.\thinspace Willem are improved. Notice that \(a\) and \(W\) are not supposed to be periodic in \(t\) and that the standard Ambrosetti-Rabinowitz assumption upon \(W\) is weakened.