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In this study, we establish existence and uniqueness theorems for solutions of second order nonlinear differential equations on a finite interval subject to linear impulse conditions and periodic boundary conditions. The results obtained yield periodic solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.

Seventy-five years of global analysis around the forced pendulum equation

Mawhin, Jean (1998)

Proceedings of Equadiff 9

Sharp inequalities for periodic functions.

Li, Jing-wen, Wang, Gen-qiang (2005)

Applied Mathematics E-Notes [electronic only]

Singular periodic problem for nonlinear ordinary differential equations with $φ$ -Laplacian.

Polášek, Vladimír, Rachůnková, Irena (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Small amplitude critical periods in a cubic polynomial system.

Toni, Bourama (1999)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Small time periodic solutions of fully nonlinear telegraph equations in more spatial dimensions

Milan Stedry (1989)

Annales de l'I.H.P. Analyse non linéaire

Sobre la ecuación matricial d/dt X(t) = A{t)X(t) + X(t)B(t) + C(t) con coeficientes periódicos.

Vicente Hernández García, Lucas Jodar Sánchez (1987)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Solution with periodic second derivative of a certain third order differential equation

Ján Andres (1987)

Mathematica Slovaca

Solutions of Minimal Period for a Class of Convex Hamiltonian Systems.

Antonio Ambrosetti, Giovanni Mancini (1981)

Mathematische Annalen

Solutions périodiques de systèmes hamiltoniens sur des surfaces d'énergie étoilées

J. M. Lasry (1982/1983)

Séminaire Équations aux dérivées partielles (Polytechnique)

Solutions périodiques des systèmes non conservatifs périodiquement perturbés

M.N. Nkashama (1985)

Bulletin de la Société Mathématique de France

Solutions series for some non-harmonic motion equations.

Chouikha, A.Raouf (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Solvability of a forced autonomous Duffing's equation with periodic boundary conditions in the presence of damping

Chaitan P. Gupta (1993)

Applications of Mathematics

Let $g$ : $𝐑 \to 𝐑$ be a continuous function, $e$ : $[0, 1] \to 𝐑$ a function in $L^{2} [0, 1]$ and let $c \in 𝐑$ , $c \neq 0$ be given. It is proved that Duffing’s equation $u^{''} + c u^{'} + g (u) = e (x)$ , $0 < x < 1$ , $u (0) = u (1)$ , $u^{'} (0) = u^{'} (1)$ in the presence of the damping term has at least one solution provided there exists an $𝐑 > 0$ such that $g (u) u \geq 0$ for $| u | \geq 𝐑$ and $\int_{0}^{1} e (x) d x = 0$ . It is further proved that if $g$ is strictly increasing on $𝐑$ with ${lim}_{u \to - \infty} g (u) = - \infty$ , ${lim}_{u \to \infty} g (u) = \infty$ and it Lipschitz continuous with Lipschitz constant $α < 4 π^{2} + c^{2}$ , then Duffing’s equation given above has exactly one solution for every $e \in L^{2} [0, 1]$ .

Solvability of a fourth order boundary value problem with periodic boundary conditions.

Gupta, Chaitan P. (1988)

International Journal of Mathematics and Mathematical Sciences

Solvability of a fourth-order boundary value problem with periodic boundary conditions. II.

Gupta, Chaitan P. (1991)

International Journal of Mathematics and Mathematical Sciences

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