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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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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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CONTINUATION THEOREMS FOR THE PERIODIC PROBLEM VIA THE TRANSLATION ÒPERATOR
Some continuation theorems for the solvability of the periodic boundary value problem associ ated to the vector differential system x' = /(£,#), are examined by means of the investigation of theExpand
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A Seven-Positive-Solutions Theorem for a Superlinear Problem
Abstract We consider the superlinear boundary value problem uʺ + aμ(t)uγ+1 = 0, u(0) = 0, u(1) = 0, where γ > 0 and aμ(t) is a sign indefinite weight of the form a+(t)−μa−(t). We prove, for μExpand
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Chaotic Dynamics for Maps in One and Two Dimensions: a Geometrical Method and Applications to Economics
TLDR
This article describes a method — called here "the method of Stretching Along the Paths" (SAP) — to prove the existence of chaotic sets in discrete-time dynamical systems. Expand
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Subharmonic solutions of the forced pendulum equation: a symplectic approach
AbstractUsing the Poincaré–Birkhoff fixed point theorem, we prove that for every β > 0 and for a large (both in the sense of prevalence and of category) set of continuous and T-periodic functionsExpand
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An elliptic problem with arbitrarily small positive solutions
We show that, for each>0, the problem pu=f(u )i n; u=0 on@ has a sequence of positive solutions (un)n with maxun decreasing to zero. We assume that liminf s!0+ F(s) s p =0 and that limsup s!0+ F(s) sExpand
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Remarks on strongly flow-invariant sets
Abstract Conditions ensuring the strong flow-invariance property for a compact set M, with respect to the differential system x′ = ƒ(t, x) , are considered. An answer to a question raised in ( Gard,Expand
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