Mohsen Timoumi, Infinite families of homoclinic solutions to nonsmooth damped vibrations with p-Laplacian nonlinearity, Vol. 2026 (2026), No. 5, pp. 1-11,

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DOI: 10.23952/jnfa.2026.5

Received March 30, 2025; Accepted December 31, 2025; Published January 28, 2026

Abstract. This paper investigates the existence of infinitely many homoclinic solutions for damped vibration systems involving the p-Laplacian. The systems under consideration are of the form
$\frac{d}{dt}\Big(\left|\dot{u}(t)\right|^{p-2}\dot{u}(t)\Big)+q(t)\left|\dot{u}(t)\right|^{p-2}\dot{u}(t)+\nabla V(t,u(t))=0,\ t\in\mathbb{R},$
where $p>1$ , $q\in C(\mathbb{R},\mathbb{R})$ , and $V\in C^{1}(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R})$ . The potential $V(t,u)$ is a combination of two functions where the associated energy functional is not continuously differentiable and fails to satisfy the Palais-Smale condition. By employing variational methods and the critical point theory, we establish the existence of infinitely many homoclinic solutions. Our results extend previous works on damped vibration systems, highlighting the impact of non-smooth energy functionals. The findings contribute to the understanding of the dynamical behavior of solutions to non-conservative systems modeled by the p-Laplacian.

How to Cite this Article:
M. Timoumi, Infinite families of homoclinic solutions to nonsmooth damped vibrations with p-Laplacian nonlinearity, J. Nonlinear Funct. Anal. 2026 (2026) 5.