Journal ArticleDOI
Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem
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In this article, the boundedness of all the solutions for the 2π-periodic equation x + ax+−bx− = f(t) is considered. But the bounded solutions are not bounded in the sense that a and b are positive constants.Abstract:
In this paper we consider the boundedness of all the solutions for the equation x″ + ax+−bx− = f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b).read more
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Boundedness for the general semilinear Duffing equations via the twist theorem
TL;DR: In this article, the authors proved the boundedness of all solutions for the periodic equation x ∈ C 19 and ω 2 x + ϕ ( x ) = G x ( x, t ) + p ( t ), where ω satisfies the Diophantine condition, and D x i D t j G ( x, t ) is bounded for 0 ⊽ i + j ⩽ 21.
Journal ArticleDOI
Historical insights on nearly 130 years of research on Paleozoic radiolarians
Taniel Danelian,Jonathan C. Aitchison,Paula J. Noble,Martial Caridroit,Noritoshi Suzuki,Luis O'Dogherty +5 more
TL;DR: The history of descriptive genus-level taxonomy on radiolarians can be summarized in five major phases: 1) initial discovery in the 1890s; 2) ignored during the first half of the 1900s; 3) renewed interest during the 1950s to 1970s; 4) the “fast” years of the late 1970s to 1990s; and 5) the early 21st century quest for the oldest and significant progress in the late Permian.
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A KAM theorem for quasi-periodic non-twist mappings and its application
Zhichao Ma,Junxiang Xu +1 more
TL;DR: In this article , the authors considered quasi-periodic non-twist mappings with self-intersection property, which depend on a small parameter and proved that for many sufficiently small parameters the mapping admits an invariant curve.
Journal ArticleDOI
BOUNDEDNESS FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING $p$-LAPLACIAN AND AN OSCILLATING TERM
Xiao Ma,Daxiong Piao,Yiqian Wang +2 more
TL;DR: In this paper, the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian and an oscillating term was studied, where the perturbation was defined by a positive constant.
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Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term
TL;DR: The existence of infinitely many generalized quasi-periodic solutions via a result of Chow and Pei from the Aubry-Mather theory of reversible mapping is obtained.
References
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Book
Solvability of Nonlinear Equations and Boundary Value Problems
TL;DR: In this article, the authors discuss the solvability of nonlinear equations and boundary value problems in the context of books and how to get a simple book that will lead to knowledge about the world, adventure, some places, history, entertainment and more.
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On the Dirichlet problem for weakly non-linear elliptic partial differential equations
TL;DR: In this article, the existence of Dirichlet solutions for weakly nonlinear elliptic partial differential equations was studied and proved for a wide variety of nonlinearities, where the nonlinearity does not depend on any partial derivatives.
Journal ArticleDOI
Quasiperiodic motions in superquadratic time-periodic potentials
TL;DR: In this paper, it is shown that for a large class of potentials on the line with superquadratic growth at infinity and with the additional time-periodic dependence all possible motions under the influence of such potentials are bounded for all time and that most (in a precise sense) motions are in fact quasiperiodic.
Journal Article
Boundedness of solutions via the twist-theorem
R. Dieckerhoff,E. Zehnder +1 more
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.