This article concerns the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation with \(p-\)Laplacian \[\Big(\left|u''(t)\right|^{p-2}u''(t)\Big)''-\omega\Big(\left|u'(t)\right|^{p-2}u'(t)\Big)'+V(t)\left|u(t)\right|^{p-2}u(t)=f(t,u(t)),\] where \(p>1\), \(\omega\) is a constant, \(V\in C(\mathbb{R},\mathbb{R})\) is noncoercive and \(f\in C(\mathbb{R}^{2},\mathbb{R})\) is of subquadratic growth at infinity. Some results are proved using variational methods, the minimization theorem and the generalized Clark’s theorem. Recent results in the literature are extended and improved.
