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Periodic-solutions of Some Forced Lienard Differential-equations At Resonance
Jean Mawhin,J. R. Ward +1 more
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On demontre des theoremes d'existence pour les solutions 2π-periodiques de l'equation x″+f(x)x'+g(t,x)=e(t), avec f continue, g Caratheodory and e Lebesgue integrable sous certaines hypotheses as mentioned in this paper.Abstract:
On demontre des theoremes d'existence pour les solutions 2π-periodiques de l'equation x″+f(x)x'+g(t,x)=e(t), avec f continue, g Caratheodory et e Lebesgue integrable sous certaines hypothesesread more
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Continuation theorems for periodic perturbations of autonomous systems
TL;DR: In this article, it was shown that the coincidence degree of the left-hand member of an autonomous differential equation x' - g(x) = 0, in the space of periodic functions with fixed period omega, can be computed in terms of the Brouwer degree of g. This result provides efficient continuation theorems specially for omega-periodic perturbations of autonomous systems.
Journal ArticleDOI
Variational methods and semi-linear elliptic equations
Jean Mawhin,Ward,Michel Willem +2 more
Journal ArticleDOI
Periodic solutions of the Liénard equation with one-sided growth restrictions
TL;DR: In this article, the existence of periodic solutions to the periodically forced scalar Lienard equation is studied, where,f, g, e: R + R are continuous functions and e(.) is periodic.
Journal ArticleDOI
Periodic solutions of forced isochronous oscillators at resonance
TL;DR: In this paper, the existence of 2π-periodic solutions for forced nonlinear oscillators at resonance is studied, the nonlinearity being a bounded perturbation of a function deriving from an isochronous potential, i.e. a potential leading to free oscillations that all have the same period.
References
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Topological degree methods in nonlinear boundary value problems
TL;DR: In this article, the index of isolated zeros of some mappings is defined as a measure of the number of isolated zero points in a set of mappings, and Bifurcation theory is applied to periodic solutions of autonomous ODEs around an equilibrium.
Journal ArticleDOI
Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Lienard and Duffing equations
J. Mawhin,J.R. Ward +1 more
Journal ArticleDOI
Asymptotic conditions for periodic solutions of ordinary differential equations
TL;DR: In this article, sufficient conditions for the existence of periodic solutions to differential equations of the form x(m) + am_ ix(m ) + * * * +alx' + g(t, x) = f(t) (m > 1).
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Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Lienard and Duffing equations
J. Mawhin,J.R. Ward +1 more