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Continuation theorems for periodic perturbations of autonomous systems
It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equation x' - g(x) = 0, in the space of periodic functions withExpand
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Periodic Solutions of Liénard Equations with Asymmetric Nonlinearities at Resonance
The existence of $2\pi$ -periodic solutions of the second-order differential equation \[ x''+f(x)x'+ax^+-bx^-+g(x)=p(t), \qquad n\in \mathbb{N},\] where $a, b$ satisfy $1/\sqrt{a}+1/\sqrt{b}=2/n$ andExpand
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A Continuation Approach To Superlinear Periodic Boundary-value-problems
This paper deals with the problem of the existence of T-periodic solutions for the first order differential system x’ = I;( t, x), (1.1) where F: [0, T] x R” + R” is a Caratheodory function. In whatExpand
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On the boundedness of solutions to a nonlinear singular oscillator
Abstract.We study a second order scalar equation of the form x′′ + V′(x) = p(t), where p is a π-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that allExpand
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Quasi-periodic solutions of a forced asymmetric oscillator at resonance
Abstract It is proved the existence of Aubry-Mather sets and infinitely many subharmonic solutions to an equation of the form u″+au+−bu−+φ(u)=p(t), where u+=max{u,0}, u−=max{−u,0}, φ: R → R isExpand
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Infinitely many radial solutions to a boundary value problem in a ball
In this paper we are concerned with the existence and multiplicity of radial solutions to the BVP whereB is an open ball in ℝK and u↦∇·(a(|∇u|)∇u) is a nonlinear differential operator (e.g. theExpand
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On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem
where the function f has superlinear growth at infinity and p grows at most linearly in u and u′. Our method is based on a continuation theorem for a coincidence equation of the form Lu = N(u, λ),Expand
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