Existence of homoclinic orbits for a class of asymptotically p-linear aperiodic p-Laplacian systems

By applying a variant version of Mountain Pass Theorem in critical point theory, the existence of homoclinic solutions is obtained for the following asymptotically p‐linear aperiodic p‐Laplacian system $\frac{d}{\mathit{dt}}(|\dot{u}(t){|}^{p-2}\dot{u}(t))+\nabla [-K(t\text{,}u(t))+W(t\text{,}u(t))]=0\text{,}$ where $p\in (1\text{,}+\infty )\text{,}t\in \mathbb{R}\text{,}u\in {\mathbb{R}}^N\text{,}K\text{,}W\in C^1(\mathbb{R}\times {\mathbb{R}}^N\text{,}\mathbb{R})$ are not periodic in t and W is asymptotically p‐linear at infinity.