We study the existence and multiplicity of classical homoclinic solutions for a class of second-order damped vibration systems of the form $$\ddot{u}(t)+q(t)\dot{u}(t)-L(t)u(t)=-a(t)\nabla G(u(t))+b(t)\nabla H(u(t))+h(t),\ t\in\mathbb{R},$$ where $L(t)$ is a symmetric positive definite matrix, $a(t)$, $b(t)$ are positive functions, $G$ and $H$ are homogeneous potentials of different degrees, and $h(t)$ is a small external forcing term. Employing variational techniques and the Pohozaev fibering method, we establish the existence of infinitely many nontrivial homoclinic solutions in the symmetric case $h=0$, and at least three such solutions when $h$ is nonzero but sufficiently small. These results generalize previous findings by addressing both subcritical and supercritical homogeneous nonlinearities in a non-periodic, non-symmetric framework.
Timoumi,M. (2026). Multiplicity of Homoclinic Solutions for Homogeneous Damped Vibration Systems. Transactions in Theoretical and Mathematical Physics, 3(1), 10-19. doi: 10.30511/ttmp.2026.2083532.1071
MLA
Timoumi,M. . "Multiplicity of Homoclinic Solutions for Homogeneous Damped Vibration Systems", Transactions in Theoretical and Mathematical Physics, 3, 1, 2026, 10-19. doi: 10.30511/ttmp.2026.2083532.1071
HARVARD
Timoumi M. (2026). 'Multiplicity of Homoclinic Solutions for Homogeneous Damped Vibration Systems', Transactions in Theoretical and Mathematical Physics, 3(1), pp. 10-19. doi: 10.30511/ttmp.2026.2083532.1071
CHICAGO
M. Timoumi, "Multiplicity of Homoclinic Solutions for Homogeneous Damped Vibration Systems," Transactions in Theoretical and Mathematical Physics, 3 1 (2026): 10-19, doi: 10.30511/ttmp.2026.2083532.1071
VANCOUVER
Timoumi M. Multiplicity of Homoclinic Solutions for Homogeneous Damped Vibration Systems. TTMP, 2026; 3(1): 10-19. doi: 10.30511/ttmp.2026.2083532.1071
