Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions

Document Type : Original Article

Author
Mohsen Timoumi
Department of Mathematics, Faculty of Sciences of Monastir Faculty of Sciences of Monastir- 5060 Monastir, Tunisia
10.30511/ttmp.2025.2071982.1063
Abstract
We investigate the existence of infinitely many fast homoclinic solutions for a
class of nonlinear damped vibration systems driven by the p-Laplacian operator. Unlike
most existing works, which typically require coercivity, periodicity, or global growth conditions
on the potential, we establish our results under weaker, localized assumptions.
In particular, the damping and stiffness terms are allowed to be non-coercive, and the
potential function satisfies local conditions near the origin. Our approach relies on variational
methods and the symmetric mountain pass theorem. Two main existence results
are obtained, illustrating the effectiveness of this method in treating strongly nonlinear
systems with nonstandard growth and damping terms.
Keywords
p-Laplacian systems
fast homoclinic solutions
nonlinear damping
variational method
symmetric mountain pass theorem
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Transactions in Theoretical and Mathematical Physics
Volume 2, Issue 4
Autumn 2025
Pages 193-203

  • Receive Date 17 September 2025
  • Accept Date 28 November 2025
  • First Publish Date 28 November 2025
  • Publish Date 01 November 2025