Homoclinic solutions for ordinary \(p\)-Laplacian systems (Q426632)

The authors study the ordinary \(p\)-Laplacian system NEWLINE\[NEWLINE\frac{d}{dt}(\left|\dot{u}(t)\right|^{p-2}\dot{u}(t))+\nabla V(t,u(t))=f(t),NEWLINE\]NEWLINE where \(p> 1\), \(t\in\mathbb R\), \(u\in\mathbb R^{n}\) and \(V\in \mathbb C^{1}(\mathbb R\times\mathbb R^{n},\mathbb R)\), \(V(t,x)=-K(t,x)+W(t,x)\) is \(T\)-periodic with respect to \(t\), \(T>0\), and \(f:\mathbb R\to \mathbb R^{n}\) is a continuous and bounded function. Under a superquadratic condition on \(W\), they prove the existence of nontrivial homoclinic orbits for such system by using a standard version of the mountain pass theorem.