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Scattered homoclinics to a class of time-recurrent Hamiltonian systems

Gregory S. Spradlin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.

Second order nonlinear differential equations with linear impulse and periodic boundary conditions

Aydin Huseynov (2011)

Applications of Mathematics

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.

Sharp estimates for the Ambrosetti-Hess problem and consequences

José Gámez, Juan Ruiz-Hidalgo (2006)

Journal of the European Mathematical Society

Motivated by [3], we define the “Ambrosetti–Hess problem” to be the problem of bifurcation from infinity and of the local behavior of continua of solutions of nonlinear elliptic eigenvalue problems. Although the works in this direction underline the asymptotic properties of the nonlinearity, here we point out that this local behavior is determined by the global shape of the nonlinearity.

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