Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations
DOI10.1007/s00605-021-01652-3zbMath1506.34058OpenAlexW4205191388MaRDI QIDQ2172587
Fabio Zanolin, Timoteo Carletti, Gabriele Villari
Publication date: 16 September 2022
Published in: Monatshefte für Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00605-021-01652-3
Brouwer fixed point theoremgeneralized Liénard equationsnon-autonomous systemspositively invariant sets
Periodic solutions to ordinary differential equations (34C25) Applications of operator theory to differential and integral equations (47N20) Nonautonomous smooth dynamical systems (37C60)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence and uniqueness of limit cycles for generalized \(\phi\)-Laplacian Liénard equations
- An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
- Periodic solutions of the forced relativistic pendulum
- On non-linear differential equations of the second order. III: The equation \(\ddot y - k(1-y^2) \dot y +y=b \mu k\cos (\mu t + \alpha)\) for large \(k\), and its generalizations. IV: The general equation \(\ddot y + kf(y) \dot y +g(y)=bkp (\varphi),\;\varphi = t + \alpha\)
- Extension of some results on forced nonlinear oscillations
- On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite
- Periodic solutions of some autonomous Liénard equations with relativistic acceleration
- Criteri di esistenza di soluzioni periodiche per una classe di equazioni differenziali del secondo ordine non lineari
- Existence and non-existence of limit cycles for Liénard prescribed curvature equations
- Existence and multiplicity results for some nonlinear problems with singular \(\phi\)-Laplacian
- A global perspective for non-conservative dynamics
- On non-linear differential equations of the second order. II. The equation \(\ddot y+kf(y)\dot y+g(y,k)=p(t)=p_1(t)+kp_2(t)\); \(k>0,f(y)\geq 1\)
- Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane
- Qualitative analysis of the periodically forced relaxation oscillations
- Resonance Problems for Some Non-autonomous Ordinary Differential Equations
- Existence of limit cycles for some generalisation of the Liénard equations: the relativistic and the prescribed curvature cases.
- A Simple Second Order Differential Equation with Singular Motions
- On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large
- A second order differential equation with singular solutions
This page was built for publication: Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations
