Existence of homoclinic orbits for a class of asymptotically \(p\)-linear aperiodic \(p\)-Laplacian systems (Q434677)

The authors of this paper investigate the asymptotically \(p\)-linear aperiodic \(p\)-Laplacian system NEWLINE\[NEWLINE\frac{d}{dt}(|\dot{u}(t)|^{p-2}\dot{u}(t))+\nabla[-K(t,u(t))+W(t,u(t))]=0,NEWLINE\]NEWLINE for some functions \(u,K,W\) and \(p>1\). An interesting result with respect to homoclinic orbits is obtained in this system.