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We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.
We prove the existence of multiple periodic solutions as well as the presence of complex profiles (for a certain range of the parameters) for the steady-state solutions of a class of reaction-diffusion equations with a FitzHugh-Nagumo cubic type nonlinearity. An application is given to a second order ODE related to a myelinated nerve axon model.
We prove the existence of bounded solutions to second order differential equations of Liénard type under asymptotic conditions generalizing recent results of Ahmad and Ortega.
A priori bounds and periodic solutions for a class of planar systems with applications to Lotka-Volterra equations
The existence of periodic solutions for some planar systems is investigated. Applications are given to positive solutions for a class of Kolmogorov systems generalizing a predator - prey model for the dynamics of two species in a periodic environment.
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