We investigate the existence of in finitely 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.
Timoumi,M. (2025). Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions. Transactions in Theoretical and Mathematical Physics, 2(4), 193-203. doi: 10.30511/ttmp.2025.2071982.1063
MLA
Timoumi,M. . "Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions", Transactions in Theoretical and Mathematical Physics, 2, 4, 2025, 193-203. doi: 10.30511/ttmp.2025.2071982.1063
HARVARD
Timoumi M. (2025). 'Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions', Transactions in Theoretical and Mathematical Physics, 2(4), pp. 193-203. doi: 10.30511/ttmp.2025.2071982.1063
CHICAGO
M. Timoumi, "Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions," Transactions in Theoretical and Mathematical Physics, 2 4 (2025): 193-203, doi: 10.30511/ttmp.2025.2071982.1063
VANCOUVER
Timoumi M. Infinitely Many Fast Homoclinic Solutions for Nonlinear Damped Systems Involving the p-Laplacian under Local Conditions. TTMP, 2025; 2(4): 193-203. doi: 10.30511/ttmp.2025.2071982.1063
