Topological degree and boundary value problems for nonlinear differential equations

Mawhin, Jean

doi:10.1007/bfb0085076

Cited by 204 publications

(156 citation statements)

References 80 publications

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“…Similar results concerning the first-order equation were obtained by J. Mawhin [13], and more recently by the authors [3] based on singularity theory and A. Tineo [19]. For the multiplicity results concerning the forced pendulum equation, one can refer to [8,10,17].…”

Section: Introductionsupporting

confidence: 73%

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

Hong-bin

2007

Proc. Amer. Math. Soc.

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Abstract. We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities,where a and c > 0 are positive constants and h(t) is a positive T -periodic function. We obtain sharp bounds for h such that ( * ) has exactly three ordered T -periodic solutions. Moreover, when h is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable.

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Section: Introductionsupporting

confidence: 73%

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

Hong-bin

2007

Proc. Amer. Math. Soc.

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“…is invertible, we denote the inverse of that map by [22]). Let L be a Fredholm operator of index zero and let N be L-compact on Ω.…”

Section: + P(t)y + Q(t)x + R(t)mentioning

confidence: 99%

Existence Results of l-Point BVP for Higher Order Differential Equations with One-Dimension p-Laplacian

Liu¹,

Gui²

2008

Journal of Applied Analysis

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“…The idea of dividing in two classes the set of correctors of a Fredholm operator is already present in Mawhin (see [10] and [11]) and Pejsachowicz-Vignoli ( [13]). In [3] the reader can find a comparison between these approach and our one.…”

Section: Orientable Mapsmentioning

confidence: 99%

Orientation and Degree for Fredholm Maps of Index Zero Between Banach Spaces

Benevieri

2001

Nonlinear Analysis and Its Applications to Differential Equations

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We define a notion of topological degree for a class of maps (called orientable), defined between real Banach spaces, which are Fredholm of index zero. We introduce first a notion of orientation for any linear Fredholm operator of index zero between two real vector spaces. This notion (which does not require any topological structure) allows to define a concept of orientability for nonlinear Fredholm maps between real Banach spaces.The degree which we present verifies the most important properties, usually taken into account in other degree theories, and it is invariant with respect to continuous homotopies of Fredholm maps.

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Topological degree and boundary value problems for nonlinear differential equations

Cited by 204 publications

References 80 publications

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities

Existence Results of l-Point BVP for Higher Order Differential Equations with One-Dimension p-Laplacian

Orientation and Degree for Fredholm Maps of Index Zero Between Banach Spaces

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